What was warfare like during the Three Kingdoms period in China?

It depends on the region. For instance, the Northern and Northwestern armies were extremely deadly at horse and horsebow warfare. The Xiliang Army in particular were know for their prowess. The armies in Southeastern China were known for their skills in naval warfare, in this case the armies of Wu and Liu Biao. The central plains region was known for their spearmen and pikemen. In general, every army brought archers with them. They would often shoot behind the main army into the enemy forces.

The Art of War was extremely influential in battle tactics, formations, strategies and troop management. If you find a strategy in the Art of War you'll likely find an example of it being used in the Three Kingdoms era. It's difficult to generalize combat in the Three Kingdoms era, but usually you had armies split into different ranks, lead by different generals. These different ranks would have different targets in order to sweep enemy territory more effectively. During these attacks it was always critical to have a supply line and depot. Having food was the most critical element to a successful campaign. Infamously, Yuan Shao lost the Battle of Guandu due to Cao Cao raiding his supply at Wuchao. In another instance, Zhuge Liang often had to retreat from his Northern Campaigns due to a lack of food.

While there is no comprehensive book on how battles took place, often it was just about charging the enemy lines and trying to break their formation. Battles could last days or just a handful of hours. The various armies used Calvary, horse drawn chariots, archers, spearmen, pikemen and swordsmen. Naval battles are a little trickier because there weren't many but from what I've gathered, they were generally filled with archers who would fire on each others boats. Once ships got close enough to each other, armies would board each others boats and fight sword to sword. Seige warfare used towers to shoot onto the walls of the enemy and also creates easy access to their walls. They would also use ladders to scale walls, rams to knock open the city gates and catapults to knock down enemy targets such as archer towers or destroy walls.

Fire was also a common strategy as seen in the famous Battles of Chibi and Yiling (Xiaoting). I've never been able to confirm if soldiers used fire arrows however. For what its worth, the TV series Three Kingdoms (2010) had soldiers sneak into the camps and burn everything with torches during the Battle of Yiling.

Also contrary to popular belief, duels between generals were not common.

Hope this is what you were looking for.