As soon as Jack joins your crew, you need to start speaking with her at every opportunity when you are aboard the Normandy. Eventually, Kelly will tell you that Jack would like to speak with you, so head down to her little hidey-hole in Engineering. Jack will tell you that she would really, really like to go to the Cerberus facility where she was held prisoner - and blow it right the hell up.
The mission indicator will now show up on your galaxy map, so go there. The mission is straight-forward, so just work your way through until you reach Jack's cell. Ask her about the objects in the room to get a cutscene and a ride back to the Normandy.Be warned: If you have already completed Miranda's loyalty mission, it is possible to lose the loyalty of either Jack or Miranda when you return to the Normandy. This can be avoided if your Paragon is higher than your Renegade. You will also lose the chance at a relationship with the character you alienate. You can regain the loyalty of the character you alienate later, but only if you have a high enough Paragon/Renegade rating.
EDIT: Thanks to Billy Horrible
for providing the following information. I will include his entire comment here, because it's rather involved:You can avoid losing either if Paragon or Renegade is high enough (Paragon doesn't need to be higher, I have Renegade twice the ammount of Paragon).
Once you're butting in on them, there are both a Paragon and a Renegade option (those things on the left in blue and red) that will be available if your corresponding skill is high enough. I was able to tell them both to shut the hell up, and they both remained loyal.
Only if neither skill is high enough you have to choose sides, but if you assign squad points to that skill that doubles your Paragon/Renegade and stick to one of the two during the first half of the game, you should be fine.