The main kind of ship was the galley, it was moved with boat men and used the wind only ocasionally. The venetian-genoese wars are a great example on naval warfare at that time in the Mediterranean as they were the main powers there. One good example of a battle is the battle of Curzola in 1298.

The main way of fighting was assaulting the enemy's galley as gunpowder was not there for making the difference. In a battle they used to position their vessels in lines and tried not to lose cohesion, one tactic invented by the genoese that was used sometimes was to fix the ships between them creating a big platform where the sailors could go from one ship to the other for focusing strenght where needed. It was dangerous because it made the ships vulnerable to storms and the venetians lost a fleet in this way trying to imitTe the genoes tactic.

A history of Venice from Norwich is a great book about that time and the Mediterranean history in general.

The following comes from an account of the naval battles fought during the siege of Constantinople in 1453:

The Turkish fleet under Baltaoğlu’s command thus con¬sisted of a number of vessels from all the shores of the Marmara, the Bosporos, and the Black Sea. Among them were triremes, biremes, fustae, parandaria, and galleys. As we shall find these terms recurring, it will be well to realize what they signified. The trireme of the fifteenth century was a long and fast vessel which had usually two masts, was very low in the water and, though employing sails, was mainly dependent for propulsion on her oars. The arrange¬ment of oars from which she derived her name was not in tiers one above the other and thus requiring oars of different length. The “banks” or benches, unlike those in ancient ships, were all on the same level. The oars were short and all of the same length: but three oars projected through one rowlock port, each oar working on a tholepin. “One man one oar” was the invariable rule. Three men occupied one bench or seat. Down the middle of the trireme ran a central gangway called the histodokè, primarily intended as a rest for the mast, but upon which the officer passed to and fro to keep time for the oarsmen. There were thus three upon each side of him, or six men nearly abreast throughout the length of the trireme. The arrangement upon a bireme was of a similar character, except that two men instead of three occupied one bench. There was also but one mast. The fusta resembled the bireme in having two oarsmen on each bench on each side of the histodokè from the stem to the one central mast, but only one on each side from the mast forward.

The fusta was a lighter boat than the trireme, and could thus be propelled more rapidly. The parandaria were heavy boats, probably not differing much from the sailing barges or mahoons still used in the harbor of Constantinople, the Bosporos, and Marmara. The name “galley” was in the fifteenth century applied to war vessels propelled by a single bank of long oars on each side. Leonard employs the term dromon, not, as it had been used in earlier days from about 500 A.D., as a generic term for war ships, but to indicate the large caiques, usually of twelve oars, which could not be classed as triremes, biremes, or fustae.

Probably the majority of the vessels in Mehmed’s fleet were not larger than the ordinary bazaar caiques which ply between Constantinople and distant villages on the Bosporos or the Marmara or are employed in deep-sea fishing.

Those were the ships. The actual battle tactics were somewhat similar to land battles because this was before cannon were very effective at all, much less effective at sea. Generally, boarding was the desired end result.

Five triremes attacked one of the Genoese ships; thirty large caiques or fustae tackled a second, and the remaining Genoese was surrounded by forty transports or parandaria filled with well-armed soldiers. The fight continued with great fury. The sea seemed covered with struggling ships. An enormous number of darts, arrows, and other missiles were thrown. The quantity of the latter, says Doukas, with pardonable exaggeration, was so great that after a while the oars could not be properly worked. The sea, says Barbaro, could hardly be seen, on account of the great number of the Turkish boats.

All this time the imperial ship commanded by Flatanelas, with the Turkish admiral’s ship always holding on to her, was defending herself bravely. Though Baltaoğlu would not let go, the other attacking vessels which passed under her bow were driven off with earthen pots full of Greek fire and with stones. The slaughter around her was great. For a time, indeed, the aim of the admiral and the energy of the attack seem to have been concentrated on the capture of the imperial ship. Chalkokondyles declares that she would have been taken had it not been for the help which the Genoese were able to give her; and Leonard also says that she was protected by “ours” – that is, by the Genoese ships. Probably it was in consequence of the risk which the imperial ship had run of being captured that presently the whole four lashed themselves together, so that, in the words of Pusculus, they appeared to move like four towers. Each of the four ships, however, remained during the protracted battle a center of attack in which the triremes took the most important positions, grappling them and being themselves supported by the smaller boats.