The Primary purpose built warships of the medieval and ancient world were the shallow draft, single mast, oared rams. These are the famous Greek Trireme, Roman Trireme and Medieval Galley. Functionally they were all the same.

The shallow draft meant that the ship didn't sit deep in the water, meaning it was easy to turn and maneuver. It was mainly powered by oars so it could function independently from the wind, which the single mast helped power on longer distances. The Ram was the armament and the goal was to ram and sink the enemy vessels.

The Romans in their early history were a total land power and ended up picking a fight with Carthage, the Sea power of the Mediterranean. The Romans built a huge fleet of Triremes but lacked the experience to properly maneuver in battle. The Romans fixed this by adding a ramp called a Corvus. The Romans would pull up next to a Carthaginian ship, drop the Corvus and storm the enemy ship, killing the crew. This had the benefit of taking the enemy ship and not destroying it but the Corvus was a danger in storms and many ships were lost in rough seas.

The medieval galley was the same basic principle of the Greeks and Romans but without the Corvus.

But Galleys were expensive and medieval kingdoms couldn't afford purpose built ships and so the cheaper option was to conscript the merchant ships in times of war.

Merchant ships of the Medieval age were typically Cogs. Cogs were sturdy deep draft, high free board, single mast ships. Deep draft being how much of the ship was under water and the free board being how much was above the water.

Medieval commanders would fortify the Cogs by building wooden battlements on the front and back and manning the ships with archers.

The most famous battle of the medieval world was the Battle of Sluys in 1340 when King Edward III destroyed the numerically superior French fleet at little cost. The basic battle plan of the English was to group 3 ships together as a unit and fill 2 with archers and 1 with men-at-arms. The archers would pour arrows into a French ship while the men at arm got close and stormed the ship.

This kind of combat became very common until gun powder canons were easily crewed on ships. The mark of the beginning of Gun powder naval warfare was the destruction of the Spanish Armada by the English in 1588

Source: Medieval Maritime Warfare by Charles Stanton