Hi there and thanks for the question about firearms in battle. While I cannot speak to all of world history, there is one particular battle in the Middle East between the old guard Turkish fighting (sword, spear, bow) and the new gunpowder armies that would eventually become commonplace: The Battle of Chaldiran in 1514 between the Safavid Persians and the Ottoman Turks.

I should state at the outset that the "Persians" in question were actually Turks (or mostly Turks) who adopted the guise and trappings of the Persians, but retained the emphasis upon traditional "manly" warfare; becoming accomplished horse riders, bowmen (especially firing bows from moving horseback), lance/spear, and, of course, swordsmanship. THis took a lot of training, was expensive, and had a track record of being extremely effective in battle. This allowed the Shah (king) of the Safavids (Shah Ismail) to amass a lot of power despite his rags-to-power past; it was so successful that the Safavids added northern Iraq and portions of modern day Turkey (Anatolia) to their territory, where they eventually came against the Ottoman Turks.

For their part, the Ottomans they had embraced gunpowder weaponry because the training time for such weapons were much shorter than full cavalry "knights" like the Safavids had. That's not to say the Ottomans were deploying untrained fighters with guns into battle; far from it. The elite corps of the Ottoman ranks was the much-respected Janissary corp which trained endlessly for war. However, it was much cheaper and much easier to train and equip Janissaries with gunpowder weapons (as well as train them to use artillery) than it was to go a traditional route of training. The rest of the army, though, was merely gunmen and not the elite Janissary, receiving only firearms training.

When the Ottomans invaded Safavid territory, the major battle - near a place now called Chalah Ashaqi - pit the Ottomans against the Safavids in just the kind of battle you are imagining; traditional vs. gunpowder weaponry. The Ottomans' focus upon gunpowder weaponry allowed them to field a larger army (Around 60,000 men) despite not having nearly as much wealth as the Safavids (who brought around 20,000 troops). The result was devastating for the Safavids; they lost 1/3 of their army due to Ottoman use of gunpowder muskets, artillery, and barricades (overturned wagons) to prevent close-quarter combat. The Ottomans would go on to conquer huge swaths of territory by employing pretty much the same tactics over and over again, until they got to Northwest Persia (modern day Iran). Incidentally, Shah Ismail retreated from governing the Safavids, turning to alcohol in the throes of deep depression, leaving his empire to be governed by visirs and advisers (who immediately began phasing in gunpowder weapons and training of their own).

For more on the Middle East and the rise of the Ottoman "gunpowder" empire, I'd recommend:

Osman's Dream: The History of the Ottoman Empire By Caroline Finkel

Lords of the Horizons: A History of the Ottoman Empire by Jason Goodwin

(EDIT) for clarity and spelling.

To take /u/VetMichael's great answer to the high seas, we have the Japanese-Korean of 1592. The Japanese navy utilized the old staple of naval warfare : hand to hand combat. Their ships were more floating platforms to fight from than proper military vessels as we would modernly understand it. Almost every single ship in the first few years of the war on the Japanese side lacked any sort of cannon, and was fast but only in the direction dictated by the wind. All the better to fight man to man with swords and arrows, like proper warriors.

The Koreans, despite bungling leadership at the highest levels and an ineffectual land military, had honed their teeth for years against Japanese pirates and unlike the Japanese navy were loaded down with cannon. Manoeuvrable enough to bring a broadside to bear quickly, fast enough to escape Japanese attempts to grapple their vessels and force a melee, long enough range they could sink Japanese ships far beyond the reach of arrows or the few muskets the Japanese sailors had. Some of the most lopsided naval victories in history are from this war, with a few dozen ships fighting against literally hundreds and emerging victorious.

For a sense of how surprising the new reality of cannon-based naval warfare was, you need only look at the repeated failures of Korean commanders to realize the importance of destroying the enemy at range. Many times what should have been a lopsided Korean victory was thrown away by charging into Japanese vessels and negating the Korean technological edge. Only a handful, like Yi Sun-sin, recognized their ships couldn't be defeated if they were cautious and kept at a distance.

The Battle of Nagashino in 1575 was considered to be something of a turning point in Japanese warfare. The Japanese had already possessed the arquebus for some time, but in the 16th century organized ranks and tactics for arquebusiers was something everybody was still figuring out to some extent. Nagashino is essentially where they got figured out.

The 1570's were perhaps the height of the Sengoku, or Warring States period, and the beginning of the unification, with several large houses contending for the Shogunate. One of the biggest houses was the Takeda Clan, which ruled The province of Kai. Their most famous Daimyo Lord, Takeda Shingen, was known to be one of the very best field commanders in existence. He and the Daimyo of Echigo Province, Uesugi Kenshin, were quite nearly legendary at times. (This was especially true when they fought each other.)

The biggest innovation attributed to Shingen was the famed Takeda Cavalry. Cavalry, of course, is an expensive sort of army to field, and at the time the Takeda were one of the few clans financially able to utilize full cavalry units. At the time the Takeda Cavalry was seen as one of the best armies in Japan, if not the best army in Japan.

Unfortunately, the Takeda Cavalry and even the Takeda Clan didn't survive Shingen long. After his death, his campaigns were taken up by his son, Takeda Katsuyori, around the same time that the Oda Clan began what would eventually be the full unification of the nation.

One of Oda's most important retainers was a man by the name of Tokugawa Ieyasu, the man who would go on to finish the unification and establish the Tokugawa Shogunate. (The shogunate would last until the Meiji restoration.) At one point during Katsuyori's campaigns, one of Tokugawa's castles posed a threat to Takeda supply lines. Katsuyori decided to take the castle, and while it was under siege the commander, one Okudaira Nobumasa, sent to Tokugawa for aid, and he in turn sent to the Oda. Eventually, Tokugawa Ieyasu and the Daimyo of the Oda Clan himself, Oda Nobunaga, arrived at Nagashino Castle to confront Katsuyori and his famous Cavalry. Aside from the battle of Okehazama (the battle the put Nobunaga on the map, so to speak), this was perhaps the most significant battle of Nobunaga's career.

To start, Oda ordered large palisades be built on the steep slopes of the Rengogawa, the largest stream in the vicinity of the castle. The palisades were built to allow arquebus fire and pikes to pass through, but did not allow horse to pass. They were set up in a staggered pattern, leaving some intentional gaps meant to channel and bottleneck any forces that made it far enough. He then ordered that infantry be equipped with especially long pikes, to help turn back any cavalry that made it as far as the palisades.

The arquebusiers were arranged in what would eventually become a standard battle line for musketeers, three ranks that rotated to achieve continuous volley fire. The sturdy defense of the front line, bolstered by the presence of Nobunaga's own elite bodyguard, prevented infantry ranks breaking during the cavalry charges, and the continuous arquebus fire caused devastating losses. By mid afternoon, the battle became a rout in favor of the Oda. In one fell swoop, the Oda Clan introduced both arquebusier tactics and anti-cavalry tactics, effectively eliminating one of the biggest contenders for the shogunate. After the battle, what remained of the Takeda fell into steep decline.

I would like to point out that after Nagashino, Takeda's longtime rival Uesugi Kenshin turned against the Oda Clan, whom he was formerly allied with. Even as enemies Uesugi Kenshin and Takeda Shingen had always had a profound respect for each other, and Kenshin was known for holding personal honor in high priority. Oda, on the other hand, was seen by many as being dishonorable in his tactics, and his success was often attributed to this. Because of this, Uesugi Kenshin confronted Oda and his top generals at the Battle of Tedorigawa, where things were equally one sided. However, this time the battle went against the Oda Clan, with Kenshin routing the Oda decidedly very early on in the fight. The loss was significant enough that the Oda Clan made no challenges against Echigo Province or any Uesugi holdings again until Kenshin's death from cirrhosis in 1578. When he learned of Kenshin's death, Oda Nobunaga was said to have remarked, "Now the empire is mine."

I fuckin' love the Dragon of Echigo.

Here's another example from when the Aztecs first encountered firearms. It's a description from the Florentine Codex, chapter 7, which relates a description of Spanish gunpowder-weapons, given to the Aztec ruler Motecuzoma by his emissaries.

He was even more amazed to hear how, on their orders, lightning would fall, that could be heard as a stroke of thunder, when the shot falls it makes people as if stunned, it deafens their hearing. And when the shot falls, and the ball shoots from the inside of the cannon to the outside, it emits a finely divided rain of fire, like spittle flying from the mouth, so it emerges. And the smoke that emerges stinks strongly of sulphur and scorches people's hair. And where the ball hits the mountain, it is as if it bursts open, it crumbles, and where the ball hits a tree, it splinters and breaks inexplicably as if someone blew it over. [...] And when Motecuzoma had heard this, he was full of fear, it was as if he was paralysed, he was greatly worried, he was concerned.

And from the 22nd chapter, when battle is joined:

And they, the Spaniards, go and shoot their metal arrows and their firearms, many people are shot through or get hit by balls. The crossbowman aims very well with the arrow, he aims the arrow very accurately at whom he will shoot. And the metal arrow makes a whirring noise as it descends, as if it is whizzing, strongly wheezing. But nowhere do the arrows miss their targets, all shoot someone through, all come to hit someone in their insides. And the firearms, the arquebuses and the cannon, they come straight at the people, they are aimed precisely at the people. But when the shots fall, all go flat to the ground, flat to the ground they seek cover, as if on sleeping pallets all are put down flat, unexpectedly the shot goes over the people, entirely unsuspected they kill people, everywhere they strike people die, where they hit someone in their passage, possibly in his forehead, or in his neck, or in his heart, or in his chest, or in his insides, or in his belly. But if they are merely hit in their thigh or in their shoulder, then they do not die from that, then they do not fall in mortal danger, but they heal again. But when the Mexicans saw how the shots fell, they went from the one side to the other going forwards, paying close attention, and very carefully.

Translation from the Nahuatl by Rudolf van Zantwijk, from his 1992 work "Oorlog tegen de goden," re-translated by me from Dutch into English. Which may have some inaccuracies because of it, but it's the version I have access to.

Like I said, this is from the so-called "Florentine Codex." The author's name is not known, but he was from Tlatelolco, next to Tenochtitlan itself, and was an eye-witness to these battles according to van Zantwijk. It should be noted that the author was also kinda biased against Motecuzoma.

Ah, gunpowder, one of the Four Great Inventions!

So by the 5th century Chinese alchemists had taken into account the properties of saltpeter and begun work in refining it, then gunpowder is referenced in the 9th century in the but Daoist book Zhen Miaodao Yaolue, the first surviving formula to it actually being combined with sulfur and charcoal (among other ingredients) wouldn’t be until the 11th century in the book the Wujing Zongyao, or the “Collection of Most Important Military Techniques,” which was compiled under the sponsorship of Emperor Renzhong of Song.

This early form of gunpowder actually contained too little saltpeter to create much of an explosion (it sets it at about 55% saltpeter, 20-25% sulfur, and charcoal at 23-25%, compared to the modern mix of 75/15/10, respectively), but it did burn quite well (Needham). So while it could shoot a projectile more than a few feet, it could still be weaponized. One of the earliest weapon formats we might think of as “gun-like” (rather than a bomb, or an incendiary, or a rocket assist to arrows) would be the fire lance, or huoqiang. The fire lance was a spear equipped near the blade with one or two hollow bamboo cylinders packed with gunpowder and one or several small projectiles. Here’s an example. In close-quarter combat, the spear could be triggered to daze, wound, blind, or even kill an enemy. Since the Song Dynasty was facing down invading horsemen of the Asian steppe, it proved very effective as a defensive weapon against besiegers attempting to scale walls, or holding breach-point in a defensive line, and also would have been a source of powerful psychological warfare.

Rocketry would be one of the first long-range uses of gunpowder in its own right. From the Needham translation of the Huolongjing (Fire Dragon Manual):

One uses a bamboo stick 4 ft 2 in long, with an iron (or steel) arrow–head 4.5 in long...behind the feathering there is an iron weight 0.4 in long. At the front end there is a carton tube bound on to the stick, where the 'rising gunpowder' is lit. When you want to fire it off, you use a frame shaped like a dragon, or else conveniently a tube of wood or bamboo to contain it.

image

Further gunpowder weapons would also be employed against (and eventually by) the Northern invaders the Book of Song describes the huopao (cannon) (from Partington):

The Sung Shih reports that in 1277 Lou Ch'ien-Hsia ordered his men to bring up a huo p'ao. "He lit it and a clap of thunder was heard, the walls crumbled, and smoke covered the sky. Many soldiers outside (en dehors) died of fright. When the fire went out, they went inside and failed to find even the ashes of the 250 defenders; they had disappeared without trace." This is obviously an exaggeration (the effect is impossible) but the small core of fact in the account suggests that a chen t'ien lei like that of 1232 is concerned.

Early barrel or shot-guns were also developed and employed. From Saunders:

In 1259 Chinese technicians produced a 'fire-lance' (huo ch'iang): gunpowder was exploded in a bamboo tube to discharge a cluster of pellets at a distance of 250 yards. We are getting close to a barrel-gun. […] in the two Mongol invasions of 1274 and 1278 ‘fire-barrels’, possibly guns with iron barrels fired by gunpowder, were employed along with the traditional catapults and incendaries.

it is thought that this image depicts such a weapon being employed against samurai

(As an aside, if you watch the Netflix show Marco Polo Chancellor Jia Sidao rather hilariously uses one of these against the Song Empress Dowager, using a smashed-up porcelain vase as ammunition)

Nevertheless, gunpowder would prove unable to spare China from conquest by the rise of the Mongolian Khannate of the 13th century. And with the conquests of first Northern, and later Southern China and the subjugation of its people to the Mongol khans, the Khannate gained access to gunpowder weapons for themselves, which they turned against the Islamic Caliphate of Baghdad and Eastern Europe. Again from Partington:

the Persian chronicler Vassaf (al Wassaf; fl. A.D. 1303-28), a protege of Rashid al-din, reported that the Persian Khtan Uljai'tu in Syria collected in 1313 and army to fight the Egyptians with stone-throwing machines, armour from Europe, archers from Baghdad, bottles of naphtha, and pyrotechnists from China... After defeating the Kipchak Turks (Cumans), Bulgars and Russians, the Mongol army under Subutai took Cracow and Breslau, and on 9 April 1241, defeated a German army under Duke Henry of Silesia at Liegnitz. The Mongols under Batu defeated the Hungarians under King Bela IV at Mohi on the Sajo on 11 April 1241. Prawdin says:...Romocki mentioned that a "flying dragon" was used at Liegnitz in April, 1241, by the Mongols, and the chroniclers speak of a "[fire-breathing head].

European account tell of similar employments by Batu and Ogedai Khan (Patrick):

D'Ohsson's European account of these events credits the Mongols with using catapults and ballistae only in the battle of Mohi, but several Chinese sources speak of p'ao and "fire-catapults" as present. The Meng Wu Er Shih Chi states, for instance, that the Mongols attacked with the p'ao for five days before taking the city of Strigonie to which many Hungarians had fled: "On the sixth day the city was taken. The powerful soldiers threw the Huo Kuan Vets (fire-pot) and rushed into the city, crying and shouting.34 Whether or not Batu actually used explosive powder on the Sayo, only twelve years later Mangu was requesting "naphtha-shooters" in large numbers for his invasion of Persia, according to Yule

It was from those conquests and occupations that gunpowder would be introduced to the Western world, and subsequently taken up and employed, and in fact the earliest Arabic references to saltpeter would call the substance namak shura chini , or “Chinese Marsh salts”

Nevertheless, over the course of the occupation-turned-Yuan Dynasty, Chinese chemists would continue to research and perfect the potency of the substance. By the time of the Ming Dynasty in the mid-14th century, they had achieved the highest-level of saltpeter concentration (as high as 91%) for maximum explosiveness.

Cited

Needham, Joseph. Science and Civilisation in China: Military technology: The Gunpowder Epic. (1987).

Patrick, John Merton (1961). Artillery and warfare during the thirteenth and fourteenth centuries. Volume 8, Issue 3

Partington, James Riddick (1960). A history of Greek fire and gunpowder

Saunders, John Joseph (2001). The history of the Mongol conquests

Didn't the British (had guns) try and fight the Zulu (had spears) and get their asses handed to them??