Just like armies, ship technology has to be unlocked. ALL ships, except for frigates, require a power source to use - the most common being oil.
Frigate - Standard, all-rounder. Can be used for transporting troops to battle. Not very sturdy, though, and easily taken down by the other ship types. Doesn't require a power source to use, so you'll always be able to use frigates. Very quick to build, too, and cheap to run! 3 units capacity
(LOCKED)Battleship - Big mother fuckers, lots of guns. Hefty and expensive. Use these to sink other ships, like... really fast.
(LOCKED)Aircraft Carrier - Mobile airbases. Provides excellent support to armies on land, fairly sturdy and great at taking out enemy subs.
(LOCKED)Super Carrier - BIGGER mobile airbases. Provides even better support to armies on land, very sturdy and great at taking out enemy subs and other Carriers.
(LOCKED)Airbourne Carrier (ABC's) - Mobile airbases capable of moving on both land and sea, and transporting armies without them losing attrition or over otherwise impossible terrain. Rare and quite vulnerable.
(LOCKED)Assault Ship - Fantasticly fast transport ships for armies. Allows armies to embark or disembark from land to sea safelty without needing a naval port. Essential if you want your army to reach its destination alive.
(LOCKED)Submarine - Battleship killers! Very sneaky. Vulnerable to aircraft carriers, though.
(LOCKED)Flagship - Colossal ships, with stronger battle effectiveness than Battleships and greater aircraft/transport capabilities than Super Carriers. These take a long time to build and soak up your economy when launched, but can knock an entire fleet out on their own. They require either a Blacklight or Uranium resource to build and use.