When reading books and viewing lectures on the subject I find a consistent trend of historians leaving out anything other than vague descriptions of conquistador tactics during events such as Cortes’ campaign in Mexico. Obviously battles and tactics and weapons are not the most crucial part of such an important time in history and usually I look at that sort of thing last but now I just have to know!
I know during the siege against the Aztecs/Mexica the conquistadors had a large force of native allies but prior to that the Spanish fight numerous battles on their own while being outnumbered. Obviously the technology advantage (guns, steel armor, horses etc) was important but how exactly did they use those advantages? All I ever seem to find is something along the lines of “Spanish had guns, shot guns, enemy dead, Spanish win” or something equally vague. Do we know what tactics the conquistadors employed in these battles? If so what were they? Thanks!
To start, I believe u/400-Rabbits is an absolute top tier Aztec expert around here and did an incredibly useful podcast on the Aztecs in general:
That said, I can contribute somewhat. Hugh Thomas's book Conquest goes somewhat into this topic and is likely of interest. To understand the differences between the Castillians and the Mexica (Aztecs) you have to start by understanding that both sides dealt with war in totally different ways. For the Mexica, the point of war was to take prisoners who could then be sacrificed. Taking prisoners was in and of itself a critical way for warriors to gain status and rank. IE the more prisoners you took the more you advanced within the military.
Now, the Castilians on the other hand, had very little interest in prisoners outside of a few specific circumstances (ie as translators). Their goal was to kill people, and while the Aztec weapons were designed to stun and incapacitate the conquistadors weapons were designed for efficiently killing lots of people.
This inherently created a tactical imbalance in engagements. If the Aztecs had just been interested in killing Cortez flat out, they could have done that on multiple occasions during his campaign. Similarly with the rest of his men, Cortez's men would have been wiped out except that the Mexica often tried to take them all prisoners which meant casualties were surprisingly light.
For an actual case scenario lets look at the Battle of the Plains of Otumba, which you're probably familiar with if you've been reading about the Aztecs. For those that aren't, the Conquistadors have just spent the whole night waging a running street battle to escape the Aztecs in Tenochtitlan. They took massive casualties, Cortez was nearly captured, and many other Spanish actually were captured and will be sacrificed very soon. Most of their native allies are gone, they are down to 340 men and twenty seven horses and some of the Castillian's dogs. The vaunted gunpowder advantage people like to harp on was a far memory as they're pretty much out of powder. It's down to steel vs obsidian, and the Castillians are outnumbered easily ten to one, probably far more.
Now, this isn't like a fantasy battle where everyone pairs up and fights one on one. The Conquistadors are bunched up. If they get split off from the main group they are swarmed, knocked down, tied up and drug away. This helps equalize the incredible numbers disparity as the Aztecs can only come at them basically one on one. Plus, the onus is on the Aztecs to attack.
Imagine you're standing there in the Aztec ranks at Otumba. You are carrying a macuahuitl, basically a top heavy wooden club with obsidian shards as the cutting edge, and you have to attack a line of people bristling with steel blades. You can do it, but you're going to have a rough time and they sure aren't going to step forward to duel you one on one. So you and a few of your buddies have a go at it and rush forward hoping to gain a prisoner. The Castilian in front of you slashes his blade, keeping you at a distance that you can't easily bash him with your macuahuitl. He's already tired, but his sword is faster than your club, so when you step into range, his blade stabs at you and you feel a fire in your chest as the tip punches thorough your cotton armor. You're in range though and get a smash in on him, but your club glances off his steel helmet.
You stumble back and one of your warrior friends helps you stagger away. You see the conquistador looking exhausted and dazed but he's still standing while you are coughing up blood. The friend who is helping you away has a nasty cut on his leg, and the other one tried to grapple the conquistador and is lying back there dead. The conquistadors are wavering but have a moment to regroup and hold the line while you bleed out and die. Bummer.
Now you start to see how this sort of fight could play out a thousand times up and down the line. The conquistadors were wavering and exhausted but in individual battles they had a good chance of killing their opponents while the Mexica warriors had a much lower chance of killing or capturing the Spanish.
Now, with that said, at Otumba the Spanish were still losing badly and their forces are on the verge of breaking, so Cortez had to try for a particularly wild gamble. The Mexica never seem to have developed really effective anti-cavalry tactics, and so Cortez and five of his friends mounted up and quite literally charged the Mexica ranks, Helms Deep style. They battled through to the Aztec commander, who they then killed.
The leader was particularly visible because he had a prominent standard mounted to his back, and when he went down the entire army knew very quickly. So you have the morale effect of the Mexica losing their general, plus the fact that no one is not giving orders. The Aztecs still have a huge numbers advantage, but now they are a massive, disorganized force fighting against a small, but tactically coherent one and the battle falls apart. The Mexica attack peters out and the Spanish limp away to fight another day.
As you can see by now, it's not so much about gunpowder, it's about a massive difference in fighting styles and the incentives that individual soldiers have, survival vs acclaim and advancement. It's also about the smaller qualitative differences, better armor, steel weapons that are just easier to use. Plus of course organizational weaknesses on the Aztec part (This in in itself is probably worthy of a whole different answer), the ability of horses to break apart Mexica attacks, and in no small part, Cortez's personal determination to win and survive. Certainly on a campaign level, Cortez himself and his willingness to continue the fight was at several points a critical factor. These things aren't particularly special or flashy to talk about. Saying the Spanish had better hand to hand weapons isn't as cool as talking about early guns, but, generally speaking, these things made much more of a difference in the closest battles than gunpowder.
Hopefully that provides some useful information, and again, there are far better Aztec experts than myself on here, so hopefully they'll also weigh in and fill in some of the gaps in my own knowledge.