In the British navy during the period I'm interested in, those who died on board would be buried at sea. During battle the dead and even the badly wounded would often just be thrown overboard -- slipped out a gunport, etc. -- but those who might die in the normal course of events would generally be afforded a Christian burial.

Their bodies would be sewn into a hammock with a round shot or two at the feet, to make sure they would sink, and would be slid overboard after a prayer. A ship's captain could oversee a burial, or if a ship had a chaplain aboard, he would perform the divine office.