If you, while in-game, press O (not zero), you will get a dialogue. In that dialogue there's a tab called "Find Fleet", that will list all fleets that currently have playing members in the game.
You can now browse through them until you find a fleet that you think looks interesting.
When you do, Click it, and find the "Details" button. You now get another dialogue that lists all players with invite permission in that fleet (if any).
Send any of them a /tell and you will very shortly find yourself member of a fleet.