I've written on this before and so has /u/vonadler who is a walking library of knowledge on the history of Swedish warfare. I'll try so summarize it into a few crucial points and if you feel that any of them are unclear or needs further elaboration, feel free to ask.

Tactics:
Sweden fought every single battle in the Great Northern War at a numerical disadvantage. The closest they ever came to numerical equality was 1:1,2 or so. This was never a surprise to anyone. Sweden was a small nation in terms of population, it could never raise armies or recover losses to the same extent that larger nations could. To compensate for that, Sweden adopted a very aggressive tactic called "Gå på" (literally 'walk on') for both cavalry and infantry.

The standard fighting tactic for line infantry at the time was platoon firing. Basically, both sides lined up and poured fire on each other until one side broke at which point the other side might have followed up with a charge.

The standard tactic for most cavalry units of the day was to skirmish or form a caracoll (basically a huge circle where the men closest to the enemy fired their pistols, essentially forming a steady stream of fire against the enemy). Exceptions to this, like the polish hussars did exist and they taught Sweden a few very expensive lessons early on in the war.

By contrast, the "Gå på" tactic is meant to take advantage of this. For the infantry, there was no reloading in battle. A Swedish battalion would form up four ranks deep and about 150 men wide and march at a brisk pace towards the enemy. At 70 paces the two front ranks would fire and let the rear ranks through. At a mere 20 paces the new front ranks would fire again at which point the entire formation charged. After 1708 this was changed to approaching at a run and firing at 20 and 10 paces. The shock effect of this was brutal, coupled with the fact that Swedish battaltions still consisted to a large degree of pikemen and that every musketman also carried a sword it was horrifyingly effective. The general idea here is that swedish units would take relatively little damage from the first enemy volley, then approach while the enemy reloaded and fire at close range followed by a charge before the enemy could dress their lines and recover. It worked.

For the cavalry, the tactic was called "Mitt på knä, gå på" (transl. 'middle of the knee, walk on'). This refers to a tight wedge formation where you place your knee cap against the back of the knee of the rider to your left or right (depending on whether you are to the left or right of the center). The cavalry would then charge in this extremely tight formation. Firing pistols during the charge was forbidden, they were to be saved for pursuit.

These extremely aggressive tactics, coupled with with a few other factors such as effective management, competent leadership, effective light artillery and high morale and discipline served to make the swedish army a very frightening force that could punch far above its weight.

However, the Swedish army always had a crucial weakness. It was never able to recoup losses quickly. It was always in a sense a case of "win convincingly or it's all over". This is what made Poltava such a crucial turning point for the Swedish army. Losses of that kind simply could not be replaced. The Swedish Empire died on that battlefield.

I get mentioned so much in this thread I guess I need to write my own reply too. :)

First of all, let me explain how the Carolean army was set up.

During the Scanian War 1675-79, a lot of deficits, corruption, waste and incompetence had been discovered. Karl XI (the father of Karl XII) was furious over the regency that had ruled the country in his minority and the amount of royal land that had been given away or panwed to noble favourites during the reign of Kristina (and earlier as well) and seized a LOT of land. He also created a system called indelningsverket (rough translation, allotment system). Instead of paying tax, a fixed amount of peasants, a rote would instead provide a soldier, his equipment and a croft for him and his family to live on. A larger amount of farmers formed a rusthåll for a cavalryman.

These semi-professional troops met by company 6-12 times per year to practice drill, live firing (yes, the British were not alone in using live fire drill), 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). The artillery and the guard was professional.

Compared to other countries, which usually had only artillery and guard (if there was one) as professionals - and the guard often having more ceremonial duties than training duties, this created a well-organised, trained and above all rapidly available army. The men knew each other and their officers from the peace time excercises and unit cohesion was extremely high. Compare this to other countries at that time, which either raised mercenaries (mostly from the German-speaking world) or force-conscripted serfs. These troops did not have the same unit cohesion, not the same training and drill and it would take time before they could work together in larger units.

The Swedish troops had an extremely offensive doctrine. Karl XI and his son Karl XII knew that most of the killing happened once one side had started to run, and that in a charge, one side would quickly turn and run - often before melee even started. Extended melee was very, very rare. Having the more disciplined army with higher unit cohesions allowed to charge home and "tumble over" an enemy formation that did not have the same discipline and unit cohesion. Charging home was thus a very effective and decisive tactic.

The Carolean standard infantry formation was the 600 strong battalion, which had 2/3 muskets and 1/3 pikes, plus NCOs, officers, drummers and grenadiers. It was deployed in for ranks, each 150 men wide. The pikemen was deployed in the centre, with the musketeers on their flanks and grenadiers on the flanks of the musketeers. The grenadiers were among the most veteran and trusted soldiers and they kept the formation at the right width by forcing the flanks together. They also formed a cordon around the banner, the drummers and the commanding officer and his second to protect them with their bodies.

The standard tactic was to march double-quick and fire a salvo at 60 paces and 20 places (in 1708 changed to 20 paces and at 10 paces (from the enemy). There was no reloading - the first salvo was fired by the first two ranks. The two rear ranks would then march past the first two ranks and be the first ranks when firing the second salvo. The whole formation would charge, in formation and step, with rapier/short sword, pike and bayonet. At this time, the grenadiers would throw grenades into the enemy formation as well.

At this time, most of the armies in Europe had switched to platoon based firing and did not use the melee charge as a standard tactic, and only the Russians still retained the pike

The cavalry charged in a very right plow formation, If you were to the left of the center, you placed your right knee in the left popliteus of the man to the right of you. Firing pistols was strictly forbidden during the charge and only allowed in pursuit. Charging in with rapier/short sword was the standard tactic.

The cavalry focused on driving the enemy cavalry from the field and then charged the enemy infantry in the flank or rear, or, if the infantry had alreade driven the enemy away, on merciless pursuit.

At Kliszow 1702, the Swedish cavalry was thrown back by the famous Polish Winged Hussars (although they had stopped wearing the wings by that time), but reformed as the Hussars were unable to drive the Swedish infantry back, counter-charged and drove the Polish crown army, including the Hussars from the field - the Polish Hussars suffered so badly they would never again appear on a battlefield in force.

The artillery was professional, but included a much larger element of light field artillery than other armies of the time. Small 3pdr guns on light carriages could be brought with the infantry, especially after Cronstedt's reforms 1711, which introduced the anmarschbommar which allowed the artillerymen to push the gun with the muzzle against the enemy for quicker movement. These guns fired reduced prepared charges with a very high rate of fire and would shower the enemy formations with grape shot or solid ball. At Gadebusch 1712 the Swedish army moved its guns through a swamp, which the Danes and Saxonians considered impossible and arrived at the flank of the allied army - which then had to endure almost 2 hours of cannonade as they wheeled the entire army to face the Swedish army.

When war broke out 1700, the army raised 67 000 well-drilled men in two weeks, men who accomplished feats such as Narva, 1700, Klissow, 1702 and my personal favourite, the outmanouvering of the Russian Army at Grodno, 1706.

It is also important to know that generals such as Rhenskiöld and Karl XII not only understood the battlefield, but also manouvre warfare. Several times, such as Narva, where the Swedish army brushed aside the Russian cavalry at Pühajõe (it would not be part of the battle of Narva 2 Days later) and then quickly marched to relieve the fortress at Narva.

Early 1706 Rhenskiöld and Karl XII outmanouvred the Saxonians and Russians badly. Rhenskiöld feigned retreat and lured the Saxonians into battle without a large part of their cavalry and won a decisive victory at Fraustadt and at Grodno. The latter thad casualties 170:1 in Swedish favour as Karl XII not only kept the Russian army from uniting with the Saxonian one and kept both the Saxonian cavalry and Russian cavalry from the Russian army, he also outmanouvred the Russian army, forcing it back into its Winter camp - which was disease-ridden and empty of supplies. 17 000 Russians died, and about 100 Swedes in the skirmishes, the time in the camp and the desperate Russian breakout.

So, bottom line. A very, very good army with great discipline, more training than any other army at the time and great unit cohesion, very good generals that understood manouvre warfare and an offensive tactic that allowed desicive charges by both infantry and cavalry.

In addition to /u/Superplaner's post you may be interested in having a look at a post I wrote about a month back about The Aftermath of Charles XII, which includes a little bit of why he was able to win these wars in the first place.