Fins allowed fish to greatly increase speed and agility when moving about. The dorsal and anal fins control yaw. The pelvic and pectoral fins control pitch. All of the fins control roll. In addition, fins generate thrust for forward motion.
Most evidence comes from embryonic data and innervation patterns.
In fact, paired fins probably evolved several different times as there are only a few positions for the fins to function properly. However, all modern jawed vertebrates have paired appendages with at least some homologous elements. This is opposite of all other jawed vertebrates where the muscles are external to the palatoquadrates. This also indicates that jaws may have evolved twice in the evolution of the vertebrates. The head region was covered with thick dermal bone.