Are ships completely player-manned?
This is a somewhat complicated issue, so I'll be thorough.
There will be NPC ships manned entirely by NPCs—police cruisers, military vessels, civilian freighters, pirates, alien craft from other homeworlds, and so on. Normal player ships
can be completely player-manned, from single-seat fighters right up to the Idris Corvette, whose specs currently indicate a max crew of ten. The max crew for the destroyer, frigate, escort carrier, and battlecruiser are unknown, because those ships have yet to be revealed.
I say "
can be completely player-manned" because NPC hirelings can be hired to man turrets, and perhaps man other stations as well (unknown). This is in lieu of a human player, though. A human will always be able to take that seat instead.
Finally, very large ships, such as the Bengal carrier, will be able carry hundreds of players. It's presumed/implied that some NPCs will be present to give the appearance of performing "flavor" tasks around these large ships, such as cleaning hallways or performing mundane maintenance, with "actual" stations (bridge consoles, turrets, the launch-able fighters, etc.) being manned by humans.
It has been tentatively confirmed that larger ships will feature stations other than just "pilot" and "turret gunner," perhaps delegating sensors, power management, and shield management (those are just examples) to additional crewmen a la Star Trek.