I've tried sea transport using the manual's instructions precisely. It never works. I'm the British at the beginning of the grand campaign, I've got enough capacity to transport the tiny numbers that I've tried (around 600 troops from St. Augustine), but I can't make it happen. Any suggestions?
Pick a unit in a port. Select sea transport. Cursor will change into a ship. Right click with the ship at a valid destination hex. Then you get the sea transport screen, where you move the troops onto the ship. Close the form and the unit should disappear. You can check the unit status that is on the seas on the army list screen.