Ships fight one another like land units do (each is strength one), complete with support from other seas and the use of hero cards. They can support land combats provided the territory has a coast touching the sea they're in ,and they can raids to land as well. They cannot attack land, nor be attacked from land (ship can't sail throuh dirt, armies can't swim at sea). Land support does not affect ships, nor land raids. Effectively, a ship can raid coasts or provide reinforcements, but an army can't be expected to swim out to deal with boats. You cannot play a consolidate power order on ships, nor pay to own a sea. It's a sea, after all. There are no locals to provide wealth or swear fealty.
Ports are a little weird. Ships in port can attack, raid and support the neighbouring sea. The port can't be taken by ships, but if the area the port is in (say Lannisport, or Winterfell) is taken the ships are swapped for those of the occupier. They mainly exist to allow you to retake your seas. They are given orders seperately. If a special consoliodate is played on the land territory ships may be mustered into the port (in addition to whenever a Mustering card appears).