I've read Thucydides and Herodotus (more recently) and I've always imagined naval combat was primarily ramming. I've also heard it described as "land battles" at sea, as troops boarded other vessels.
For all its other faults I was wondering how true the naval combat was depicted in 300:RofaE. (Lets not even talk about the oil/fire spewing ironclad vessel). There seemed to be very little missile troops aboard either side and the Greeks were just standing on deck as easy targets (without even some structure to hide behind). How were missile troops actually employed? Did the troops who ultimately acted as a boarding party just stand on deck as easy targets?
I've not seen the movie so can't comment on it, but I can say a few things regarding naval warfare in the classical period.
There were two primary methods of combat with the ancient trireme (the cutting edge of its time):
The first required skill, you needed well trained rowers and helmsman to achieve a good hit that would allow you then to withdraw unscathed, leaving the enemy ship to flounder (being all wood, they wouldn't just sink).
The latter needed less skill since you just needed to get alongside and get your marines to kill their marines and thus seize control of the ship. The downside is this required a significant fighting force and their added weight would make your ship less maneuverable.
The Athenians opted for the former and were pretty preeminent as the naval power in Greece (whereas the Spartans were the preeminent land power).
Even Athenian ships still carried some marines and archers, I believe around 14, for defensive purposes. They could also be dismounted for amphibious operations (they did a lot of raiding in the Peloponnesian War). The marines would be trained to shoot arrows or throw spears from a sitting position for better stability.
as /u/Agrippa911 stated below, naval warfare was conducted using various methods including boarding and "fire ship" tactics, but the Athenians, naval masters of the time, much preferred trireme tactics. It should be pointed out that there were different classes of ships, some meant for "ramming," some meant for boarding, etc. One of these classes were the triremes, which were largely designed for hit-and-run tactics. The trireme, would approach an enemy vessel, and depending on the wind would engage in periplous or diekplous maneuvers. periplous was to use momentum and speed to row around the enemy, and attempt to hit them on their broadsides which is the area that would cause the most damage. It involved a sequence of back-rowing and continual ramming with the intent of causing enough damage to sink or put out of action the enemy ship. Diekplous was a head-on approach, usually only conducted if the trireme outclassed the enemy vessel, or if it had speed advantage. Generally, Athenian Strategoi would prefer to avoid this since a head-on hit would deal damage to themselves as well as the enemy, given the circumstance.
Thucydides describes large naval engagements during the Peloponnesian War, many of which centered around the Sicilian Expedition (415-413 BC). During the Expedition, the Syracuse Navy effectively combated Athenian naval superiority in a number of ways. The first was a reinforced prow on the front of the ships using a wood cut from strong local lumber, and cutting it into less of a sharp angle, and more of a block shape to not only withstand Athenian head-on attacks, but destroy Athenian prows in the process. When the Syracusans went on the offensive, they utilized diekplous tactics and destroyed the Athenian fleet during the later stages of the Sicilian Expedition. What was left was cornered in a Bay, and the Athenians made a bold move to reinforce their prows to be able to combat Syracuse effectively, then rowed straight into the enemy blockade with hopes of breaking through and sailing for home. Syracuse, however, knew this would be their plan, used a type of grappling hook that when the Athenians would make initial contact (hoping to create a gap in the formations) Syracuse would simply anchor the Athenian ships to theirs using these hooks, and slaughtered everyone on board. It was a very bloody affair, Thucydides being an Athenian himself writes it in a tragic tone. If you are interested in this topic i strongly recommend checking out Thucydide's book History of the Peloponnesian War. Penguins classic is a good version.