The short story is a well-drilled and well-trained army, extremely offensive tactics and superb discipline.

The longer story is somewhat longer.

The father of Karl XII, Karl XI inherited the crown at age 4 and was placed under a regency council. At the time of his majority in 1672, the regency council had let a substantial rot in the form of corruption, nepotism and incompetence take its place in the administration, army and especially the navy.

When Denmark declared war 1675, the Swedish armed forces were at a low Point - as was Swedish influence. Sweden was dependent on French subsidies to keep armed forces in the field, and were thus at the mercy of French decisions. Indeed, despite some Swedish victories forcing the Danish invasion of Scania back, France made peace in Sweden's name without consulting Sweden at all, treating the nation as a puppet.

This, combined with the extensive rot in the adminstration, army and navy made Karl XI furious.

The nation was ruined through the war and the long policy of Kristina and Karl XI's father Karl X Gustav to pawn off Royal land and dues for loans and for services by noble officers.

Karl XI managed to declare himself and absolute monarch and siezed all royal dues and land and introduced a new army and navy system. The state would pay for ships, the artillery and the professional guard regiments while the rolls on the Neva and Düna (Daguva) rivers paid for the garrisons and troops in Ingria, Estonia and Livonia and the tolls on the Weser river paid for the garrison and troops in Sweden's German provinces (Bremen, Wismar and Pommerania). The free-holding farmers of Sweden (who owned about 30-40% of the arable soil) would band together a few farms (depending on size) into a rote in indelningsverket (the allotment system). One rote would supply one soldier and pay for his equipment, supply him with a croft for him and his family and a meagre pay in addition to his croft. A larger group of farmers would form a rusthåll which provided a cavalryman and his horse and remounts.

The soldiers met by company 6-12 times per year to practice drill, live firing, manouvering and charging in formation. Once a year the regiment met for 2-3 weeks for larger exercises, and every 3 years, several regiments met for large-scale mock battles (this was unique at the time). A soldier would spend somewehere between 2-3 months a year in training. Regiments were raised in counties and companies in muncipalities. Officers were always present in the soldiers' lives, being instructed to take an Active part and interest in their welfare in peacetime as well as in wartime. Soldiers and officers knew each other, trained together and eventually fought together, sharing the same hardships. This created a large amount of trust and unit cohesion.

The state set up and expanded existing proto-industries to provide high-quality equipment for these troops - the rote or rusthåll was forced to buy from these industries and rigorous checks were made, with Karl XI himself repeatedly inspecting industries and regiments to weed out dimwits, drunkards, incompetents and corrupt officials. There are still a myriad of stories of Gråkappan (the grey coat) as Karl XI was called as he preferred to travel in very small groups at high speeds (riding and chancing horses rather than going by carriage) and simply dressed during these inspections. Many of these stories tell of his devotion to duty and willingness to reward those that were diligent and punish those that were lax. In one famous such story he arrives at a small town too late to be a guest at the local inn or the local offical, and decides to sleep on a bench in the square. The nightwatchman however, taking him for a vagrant, tells him off that it is forbidden. Karl XI then duly leaves, but leaves a silver coin and a praise for the nightwatchman for his devotion to his duty with his superiors.

As an example of the production of weapons we can take the Värja m/1685. A rapier that was made in about 300 000 examples for the regular soldier to carry, each blade was tested for durability by the tip being placed between a doorpost and the upper part of a door with a man supending himself from the handle. If the sword bend, but did not break, and sprung back to straight shape after being released it was considered a good quality blade. The blade was then sharpened and tested by cutting a feather in two mid-air. If it passed both tests, it was considered fit for battle.

The doctrine of the army was extremely offensive. Karl XI knew that most Soldiers died when they had started running, and forcing the enemy to run as soon as possible was the best way to limit your own casualties and increase enemy casualties. To achieve this the army needed not only an offensive tactic (always being willing to close with the enemy) but also a superior discipline and unit cohesion. The army was always on a very strict discipline, had a very high unit cohesion (due to troops and officers training together and being part of each others lives in pleacetime).

The army also had a large part cavalry - while continental armies of the era usually were 1/4-1/3 cavalry, the Swedish army were often 1/2 cavalry in the field.

The standard infantry formation was the battalion - 150 men 4 ranks deep, with the centre 1/3 being equipped with pikes and rapiers and the flanks being muskteteers and grenadiers.

The battalion would march double-quick towards the enemy and at 60 and 20 (1708 changed to 20 and 10) paces stop, have the first 2 ranks of musketeers fire a volley, the second 2 ranks marching past them and taking the vanguard until the next stop where those 2 ranks now at the front fired. Reloading was strictly forbidden. After these two volleys, the battalion would charge with bayonet and pike while the grenadiers on the extreme flansk threw hand grenades. Often these formations would "tumble over" enemy formations as they lacked pikes and were disoriented and in disorder from the close salvoes from the Swedish musketeers and were unwilling to go to melee. Continental armies of the time used fire by rank or platoon fire to maintain a steady rate of smaller salvoes. Once the enemy formation had started to run it was cut down from behind and those that got away pursued by the Swedish cavalry.

The Swedish cavalry's combat formation was the squadron, a 125-men plow-like formation. Each man on the right would place his left knee in the right popliteus of the man to the left of him and the other way around for the men on the left, creating a very tight formation of men and horses. The Swedish cavalry were equipped with rapiers, a par of pistols, a carbine and protected by a mooseskin leather coat and a steel cuirass (although the cuirasses seem to have been discarded as too Heavy and not giving enough protection after about 1701 or so). Firing pistols was strictly forbidden during the charge and only allowed during pursuit.

The cavalry was to charge the enemy cavalry and drive them from the field, pursue them and then return to the battlefield to either charge the enemy infantry from behind or pursue the enemy infantry driven from the field by the Swedish infantry.

The artillery consisted mostly of small and light 3pdr field artillery pieces that were placed in between infantry battalions to add to their firepower with cannonballs, case (canister) and grape shot. During 1710-1711, Carl Cronstedt reformed the artillery to include anmarschbommar a system where the crew (at times with the aid of infantrymen) could push the gun with bars that fastened in front of the gun, so they could move it almost at marching speed without limbering it and without turning the muzzle away from the enemy. He also introduced pre-packaged reduced weight paper cartridges for the artillery, so called geschwinda shots that allowed the artillery to fire up to 10 shots per minute (albeit at a shorter range). At Gadebusch 1712, the Swedish artillery moved through a forested swamp and arrived at the flank of the Dano-Saxonian army, forcing it to rotate under fire to reform for about 2 hours. When the Swedish army charged, the Dano-Saxonian army was so weakened by artillery fire that it broke almost immediately.

Such was the army that Karl XII inherited from his father. It was a high-quality, well-trained, well-supplies, well-equipped semi-professional force led by some of the best generals of the era, including Rhenskiöld and Karl XII himself.

It was capable of taking on the famous Polish Winged Hussars (although they had stopped wearing wings by this time) at Kliszow 1702.

Karl XII was a master of manouvre warfare. During the Winter campaogn 1705-1706, not only did he keep the Saxonian and Russian armies separate, he also separated the Russian cavalry from the rest of their army, forced their army into their winter camp (where they lacked supplies) and mercilessly pursued them as they desperately broke out through frozen swamp. Casualties were about 17 000 Russians, for about 100 Swedes.

At the same time Rhenskiöld took on a twice larger Saxonian army at Fraustadt head on. The Saxonians were entrenched, had plenty of artillery and hand mortars and were completely shattered, losing 75% or more of their force.

I wrote an answer to a similar question a while back that sort of answers your question. I'm sure there are other users who would love to have a crack at the military tactics part though. :)