Not many guys have the kind of nerve to try to get an ex girlfriend back. Well, OK, stalkers and creeps, but regular guys generally figure it was trouble enough getting a girl once. If you're here trying to find out how to go about getting back together with an ex girlfriend, it must be because she meant something special to you.
You should ask yourself if it's worth it. Look beyond the short-term to the long-term: will the same problem that came between you come back again? If you don't do something to fix it first, it most definitely will. If the problem was on your end, you know even more what to do about it. You have to be realistic and ask if you are really prepared to change that for her, because if you don't and just pretend to, it will come out and you'll both be disappointed.
If the problem was on her end, you have another situation that's more difficult. Men change for women more often than women change for men. It can be done; but you have to mean something very special to her, and then you have to pledge your support and commitment to her long enough for her to make it happen. If her problem is some kind of behavior issue, that might turn out to be a very long road indeed. Love can fix problems, but do remember that there's a difference between a boyfriend and a doctor.
You should also be careful not to let your hormones do the thinking. Yes, on cold, lonely nights it seems like paying a "bootie call" is the best idea, but that isn't what you're doing here. If you were involved with a woman before enough to be serious about her, you can't move it back into casual friends-with-benefits. It just doesn't work that way. Getting back together with an ex girlfriend implies that you had something really important between you and you want to start it again. Otherwise you'd hook up with the next random girl to come along and move on from there.
Do pay attention to whether she welcomes hearing from you again or not. If you broke up on fairly friendly terms and it's been a few weeks or months, she should at least be open to being friendly. If she greets hearing from you again with an icy reception, however, you'd better toss in your hand, because the game might just be over.