Medieval warfare was, as most warfare is, quiltet complicated, and the method with which it was waged depended a lot on the reason for waging it. I cannot give a thorough answer, as it really depends on when and where. The medieval period lasted for a thousand years, and fighting in the mountains of Austria was quite different than the viking raids in England.

Taking and holding fortresses was definitely an important part if it, as the de facto control of local strongholds helped medieval princes to keep a foothold in otherwise hostile territory, and from there exercise control over the nearby populace, or to serve as a bridgehead for further military activity. However, taking a fortress was not an easy affair, as the besieging army would be vulnerable to direct enemy attacks, as well as raids against their supply lines.

Raids was the more "normal" part of medieval warfare, and strongholds, such as classic medieval castles, were mainly meant to discourage raids, mostly by serving as a staging area for counterattacks against the raiders, while being too troublesome to conquer for a small force. The raids themselves were perhaps the most important part of medieval warfare. Primarily, they served to enrich the attacking force, while draining the resources of the defender, which meant that, when they were most successful, you ended up having the defending party pay the upkeep for the raiding army through the spoils that were taken. Secondly, the raids, when they were severe enough, also served by ravaging the land, making it less productive, and thus less important for the defender. It was a lot easier to have the losing side give up land if the land in question was worthless in the short run. Thirdly, the raids would destabilise the regime of the defenders by displacing the populace. Fugitives are always bad for the economy, as they either must be fed (as opposed to producing a surplus of food, they become a net drain on food reserves) or they would turn to brigandry, as other possibilities were exhausted. Besides the economic consequences, the entire political raison d'etre for the nobility would also be called into question. The main role for the aristocratic warrior class in Western Europe was to defend the populace, and when they were unable to do this, it might be in the interests of the populace to either look for new aristocrats to protect them (this could very well be the same people who just drove them from their lands, but could likewise be rival factions within the same realm) or to take matters into their own hands, which would lead to an armed and aggressive peasant populace, and these were often notoriously hard to tax. To sum up the raiding aspect of medieval warfare, as long as you were the attacker, you were winning, as you would usually drain a lot more of the defenders ressources, than you would your own.

While castles provided some defence against a raiding force, the real solution was to gather an army, and drive off the attacker. Armies would often attempt to have the enemy engage on unequal footing, which meant that the two opposing armies would often dance around each other for days at a time, positioning themselves on hills or by rivers, or other defensible positions, and wait for the enemy to attack. This would go on until either one of the commanders attacked the enemy, thinking their position to be exposed enough to risk an attack, or until one of the sides escaped to the safety io some nearby fortress or the like. This dance to have your army in a superior, defensible position necessitated that one's army was kept together, which meant that raiding became impossible, and suddenly the warfare would become an economic drain on the attacker.

These aspects, taking fortresses, raiding and lastly, manoeuvre warfare which could lead to a pitched battle, is perfectly exemplified in the Crecy-campaign in 1346-47. The English king Edward III had landed in France with a large army, and had raided and plundered most of Normandy, including sacking the city if Caen, and raiding the city of Poissy, around 30 kilometers from Paris (people could see the smoke of the burning villages from Paris). King Philip VI of france countered with a larger French army, which chased the English back north along the Somme River. Eventually, the English army crossed the Somme after winning a minor skirmish, and the took positions on a hill near the village of Crecy. Here, King Philip decided that the English were exposed enough in their position (he didn't have to cross a river to attack them), he also both believed that they were tired from their long march, and that he had to lunjsh them for their ravaging of the French countryside. Philip, however misjudged the superior positioning of the Wnglish, and his army was soundly defeated. While he withdrew back to Paris to muster a new army, the English successfully laid siege to the fortified port city of Calais, which surrendered after no French relief army turned up. Calais stayed in English hands until 1558, and would enable the English to safely land armies on the continent until then, which was a great strategic advantage to have against France.