You were together for over four years, and it's only been about four months and she is already dating someone else, correct? That reaks of rebound to me. Try to take a little comfort in the fact that most likely, the only reason she is with this other guy is because she is hurting over your breakup. (Don't be happy that she's hurting, of course, just that she probably doesn't have any true feelings for the other dude). The way I see it, you have two viable options, but neither will be easy on you. 1) Don't meet with her, or talk to her, or respond when she calls. IE stick with NO CONTACT. This way you can't se or hear things that are going to hurt you even more, but the possiblities are going to run through your head, perhaps driving you crazy. 2) Meet with her in a neutral setting (like a public park) and have a nice, civil conversation with her and try to hash things out. If you do this, you may hear things that you really don't want to, and you might leave even more devastated than you are now.
Zizu, please understand that a friendship in this case will not work. Why? Because your breakup wasn't mutual. You both might say you want to be friends, and it might start out ok, but the possessive feelings are going to quickly return, along with jealousy and anger that she isn't yours. In a case such as yours, the best thing to do is either stick with no contact or get back together--you shouldn't (read: can't) stick yourself in no-man's land here. If you do meet up with her to talk and try to explain everything, try to stay realistic. You will both need to work extremely hard for your relationship to work again, if indeed you are both willing to give it another shot. Whatever you do, don't beg her to come back.
On a side note, Alex can you move this thread to the Ex Talk forum, I think it is more suited for that area.