Like Vandelay said, you need to hit a flagship. Once you've made enough damage to it, green circles will appear. If more than one is attacking the ship, the boat that made that last hit will get the green circles. One you see the green circles, use you grappling hook and aim it at the circles. When you land a hook, the boat will be towed to yours. Start hitting the captain with grape shot if you have it yet. If you don't just use cannonballs. A board button will appear, and when the captain clicks on that, the crew will board the enemy ship. Once you've killed all the Navy or EITC, you will automatically go back to your own ship.
Becareful though, sometimes these ships have very high level people on board.
