Across westeros there are various types and size of watercraft in use from smaller fisher boats and raider vessels, various warships and trade ships, up to the huge war dromonds and the magnificent swan ships that cross the summer seas.
Ships in the World
As far as naval power in the Seven Kingdoms, the Major fleets are: In the west Greyjoys fleet, based at the Iron Islands, In the east royal fleet(most of it destroyed on the Blackwater) based at Kings Landing, In the south the Redwynes fleet based on the Arbor, However the North has had no strength at sea since Brandon the Burner put his father's ships to the torch hundreds of years ago.
In the rest of the Seven Kingdoms, lords whose lands abut the coast, might keep a war galley or three about, for coastal defense against pirates, but only major houses like the Lannisters might have larger and grander fleet of twenty to thirty ships. Usually for major battle, the lords would call the ships of their various bannermen, just as Stannis summoned the lords of the narrow sea for the battle on the Battle of the Blackwater. Similarly while Greyjoys main force is the Iron Fleet, it can also raise hundreds of Ironmen ships(largest fleet), however most of those will be longships made for raids rather than battle, comparable to lesser war galleys elsewhere in the Seven Kingdoms. where Larger and more formidable ships are more common like cogs, carracks, and war galleys of various sides, up to the great dromonds with scorpions and catapults on deck.
The Tyrells are in more or less the same position as the Lannisters, though they depend even more on their bannermen, especially the lords of the Shield Islands off the mouth of the Mander. The Hightowers have only a few warships, but control Oldtown, home to numerous trading vessels.
Ibben make use of Fat-bellied whaling ships, with hulls black with tar. and people of the Summer Islands use Swan ships.
Ships are constantly used in small skirmishes and we have seen full scale naval engagements, for example: Battle of Fair Isle, Battle of the Blackwater. they are also used for raiding, lords whose lands abut the coast might need to maintain war galley to defend against piracy, however it would be up to the major houses to deal with anything larger than that like the Ironborn raids encountered during the War of the Five Kings. Ship are also use for support roles providing provision, transporting troops etc.
The basic tactic of naval battles is to get the ship close enough to ram the other ship and then board her and fight the rest of the battle on the deck. Up until they close longbows and crossbows can be used and sometimes siege weapons considering few of the biggest War Galley's.
- Longships, are used as fast raiding ships on the sea and land. They can travel twice as swiftly as a merchant cog and carry about 1,000 men, specifically a hundred feet long longship would have about fifty oarsmen and room for about a 100 men on the deck.
- War Galley, are larger than normal Galleys and carry more tonnage as a result of being equipped with siege weapons like ballista or catapults, and having a larger compliment of oarsmen and soldiers onboard. The standard tactic for engaging is to disable the opposing ships' sails then ram and board it. They are presumably the kind of ship that GRRM has compared to Venetian/Byzantine dromonds of war
- Swan ship, are known to have 'red archers', companies that help defend the vessel from attack. Women serve on swan ships, and can even command the 'red archers'. 
Types of ships - Specifications
- Galleys, vessels larger than boats, that are primarily propelled by oar power. They are used for warfare, trade and piracy. Due to their low setting they were primarily coastal ships, preferring to thread through archipelagos rather than risking even a moderate sea. Their large rower crew made them maneuverable and swift but also required frequent stops for food and water. The galley has supplemental sails to replace or augment the effort of the rowers, particularly during long journeys. The ability to travel swiftly without regard to the direction or strength of the wind became invaluable for daylight expeditions across open water. (Real-life, practical upper limit for a galley fast and maneuverable enough for warfare was around 25-30 oars per side. By adding another level of oars, the galley could be made shorter with as many rowers, while making them strong enough to be effective ramming weapons.) The flagship of House Hightower, Honor of Oldtown, is an impressive four-decked galley, bigger even than a dromond.
- Longships, are smaller type of Galley, primarily used by the Ironborn. They are long, narrow, light, wooden boat with a shallow-draft hull designed for speed. The ship's shallow draft allowed navigation in waters only one meter deep and permitted beach landings, while its light weight enabled it to be carried over portages. Longships were also double-ended, the symmetrical bow and stern allowing the ship to reverse direction quickly without having to turn around; this trait proved particularly useful in northern latitudes where icebergs and sea ice posed hazards to navigation. Longships were fitted with oars along almost the entire length of the boat itself. Later versions sported a rectangular sail on a single mast which was used to replace or augment the effort of the rowers, particularly during long journeys. GRRM has compared them to Viking longboats.
- Cogs, are mostly propelled by sails, which made it difficult to sail, especially upwind, and it was hostage to breezes and currents in a way that the swift galley was not. however it could better manage rough seas and its small crew and ample storage space gave it greater freedom of movement. making it perfect for trade or equipment transport.
- Carracks, large ocean-going vessel. Stable in heavy seas, and roomy enough to carry provisions for long voyages.
- Swan ships, so called in the Seven Kingdoms for their great white sails and figureheads which are often carved in the shape of birds, are very large ocean-going vessel designed and built in the Summer Islands, with a good wind behind them can outrun any galley. However, they are helpless when becalmed. They have High-masts and high forecastles.
- Whalers, Fat-bellied ships with huge hulls black with tar from Ibben used to hunt and process whales in the Shivering Sea.
- Dromonds are among the biggest, most powerful and most expensive of the warships available in Westeros. They are probably similar to the real historical dromonds. A fleet of ten dromonds is built to replenish King's Landing sea power. House Hightower's fleet employs at least three on the fleet that protects the city, although its four-decked galley flagship, Honor of Oldtown, is bigger yet. Two other dromonds were sank by the Ironborn shortly before.
- The Iron Fleet.
- Some of the descriptions are based on real life parallels.
- SSM:The Lannister fleet (September 26, 1999)
- A Clash of Kings, Chapter 16, Bran II.
- SSM:Greyjoy fleet (February 09, 1999)
- A Clash of Kings, Chapter 63, Daenerys V.
- A Clash of Kings, Chapter 11, Theon I.
- A Clash of Kings, Chapter 24, Theon II.
- A Dance with Dragons p.523-524
- A Feast for Crows, Chapter 45, Samwell V.
- A Dance with Dragons, Chapter 40, Tyrion IX, Page 527.