Ships can be confusing at first, because there are three types of sea travel and the rules for each type are different.

1: Your agents (princesses, assassins, bishops etc.) can move from any port to any port in one move. They don't need ships to do this. I guess they just hitch a ride on any passing vessel, whether it belongs to someone's navy or not.

2: Your armies also travel any distance by sea in one move, but there are different restrictions. You only need a port in the starting province, not the province your army ends up in. You need at least one ship in each sea area between the starting province and the ending province. You don't embark your army on a ship at all. Instead you just click your army and move it to the destination province. (Sea travel without getting in a boat! Some trick.) Don't forget that your army will not be able to come back if there is no port in the destination province. Its easy to get an army trapped in Ireland.

Sometimes your army cannot travel by sea because it has been blocked. This happens when an enemy ship is in one of the seas along your army's route. It also happens if you are trying to invade a province (hostile or not) if the owner of the province has a ship along your route.

3: Trade is different yet again. In order for one of your provinces to engage in trade, it must have some kind of trade goods. Right click on a province and look at the top of its description to see if it has anything. If it does, you can build a trading post there. Building the post (or an upgraded version) lets you make a little money by taxing local trade. This happens automatically once you have a trading post. But to get decent money you have to export. For this to happen your province must have a trade post and a port as well. Then it can trade with allied or neutral provinces that have ports, so long as you have at least one ship in each sea area between your province and the province you want to trade with. Once you have met all these conditions, trade happens automatically. Hostile ships can block your trade just as they can block your armies. If you manage to connect the right province with a lot of trade partners and avoid getting your route blocked, you can make a fortune.

Note that your provinces cannot trade with each other, so conquering trade partners will wreck your trade. I'm not sure if you can trade with rebel provinces or not.