The Leviathan section of the game will automatically begin after you leave the planet where you find the third Star Map. The Ebon Hawk will be tractored aboard Saul Karath's ship, and very bad things will begin to happen.
Carth, Bastila, and your PC will be captured, so you'll need to pick one of your other teammates to hopefully escape imprisonment and rescue you, excepting Zaalbar, who obviously would have a difficult time evading capture by the Sith. Any character that you pick to be involved in the rescue will start completely unequipped, with only their skills and Force powers to rely on.
Before your impromptu excursion begins, though, you'll have to endure some torture at the hands of Saul, Carth's old mentor. Your choices here have no effect on the events to follow; you'll need to break out of the prison whether you freely offer up information, or let your teammates be tortured.
Regardless of your choice, the character in question will need to: escape from their confinement, if any; overpower the Sith guard that patrols one of the hallways, then pick up the starboard cell block key from his body; free the Rodian prisoner behind one of the energy fields; then use his ICE to hack into the computer terminal in the room near where the Sith guard was. Once you've broken into the terminal, you can open all of the cell doors in the prison, which lets out all of the Rodian crazies, then activate the emergency riot system, which will kill all of the Rodians and Sith in the hallway. You can continue to hack until you unlock the door that Carth and Bastila are behind, or just pick up the key from the footlocker in the (now empty) barracks. Regardless, head up to the holding facility and let your teammates free; they'll make a mandatory party for you, and you'll be on your way.