I prefer not to say too much about the game, as discovering the details for yourself is part of the experience. My personal thoughts about the game and its history are in the afterword, but interpreting its meaning is up to you. Everything in the game is there for a reason.
The Infinite Ocean is a Myst-style point & click adventure game. It's fairly big for a flash game, and has a lot of story, so to enjoy it you need to take your time.
You interact with the environment by left-clicking.
To turn left or right, move your mouse to the edge of the room and click on the arrow that appears.
The main menu appears at the top of the screen when you move your mouse there.
For more detailed information, read the Instructions/Help screen in the game. (Highly recommended!)