1) Use tape. If you feel like you're getting a blister or if you already have a rip, use a little bit of pre-wrap and then wrap your hand in athletic tape. It doesn't necessarily take away the pain, but it does help to prevent the blister from ripping further. (Ew, I hate the word blister. I bet you do, too. I don't blame you. Bear with me.)
2) If you are getting to the level where you're starting to learn things like clear hip handstands and giants, now is the time to get grips. They do NOT prevent rips like some people say they do, but when you are performing skills that require so much hand-to-bar time, they do reduce the friction a little bit. Of course you'll also need them to help you grip the bar, which is clearly their intended purpose.
3) If you get a callus on your hand, you can use a pumice stone or some other sort of file on it to reduce it a little bit. You don't want to go overboard with this, obviously, because if your hands are completely callus-free, they'll get sore pretty quickly on bars.
4) This one is a little controversial, but some girls like the "sock method." Put some lotion on your hand and then put a sock over it while you sleep. Take it off in the morning. Supposedly it has healing powers, though I've never tried it myself.
5) Try some Neosporin and a band-aid if all else fails.
6) If you're really in a lot of pain, ask your coach if you can work on low-friction skills for a while. Examples of that would be casts, cast handstands, squat ons, jump to high bar, pirouette drills, release moves, transitions, etc. depending on your skill level.
Happy bars. :)