Honestly, the best thing to do is to not let yourself get crossfaced in the first place, as a good crossface can be a bitch to escape once it's fully locked in. If you do find yourself in that position, though, just remain calm, guard against the mount and arm attacks like you normally would, and wait for an opportunity to slip out.
Unless it's a tournament and you're down on points (or it's training and your partner is a douche), he isn't just going to hold you there all day. Eventually he's going to try to improve his position or attack an arm, and once he does you'll have your chance to escape.