I thought I'd give you some advice on how to handle these things. You may not always win, but you'll come out looking sane/smart/less-of-a-bitch if you follow these rules. So here we go.
1. Do not call the other person names or use any demeaning adjectives towards them. This includes (but is not limited to) calling them a bitch, and asshole, stupid, an idiot, a dumbass, a douchebag, ect, ect, ect.
2. Do not bring past issues into the argument. You need to discuss what is going on right at that moment, not what's happened before.
3. Keep calm, or at least the appearance of being calm. Yelling, screaming, cursing, caps, and other things that express anger just get you no where in solving the issue. Not to mention these things normally make you look ridiculously stupid.
4. Don't bring your friends or theirs into the issue. Sure, you can ask your friends for advice as I'm sure they are, but if you have to send them to talk for you then you look like a wuss. Fight your own battles.
5. Your first instinct does not need to be to cut them off or ignore them. The first solution attempt should be talking the problem out. If you're reading this, you should be able to handle mature conversation.
6. If the other party doesn't respond to you, try again in a day. If they're mad, maybe they need time to cool down? After that point though, you might as well just give up or wait until they can grow some balls/put on their big girl panties and talk about it.
7. If you find yourself putting a lot of effort into working things out, but they're just shutting you out completely and not really working it out, give up. This shows a major flaw in their character and you should just move on.
8. Don't make the dilemma public. Third-parties tend to be biased without fact and do not think before they speak and this can lead to a lot of hurt. Especially if you haven't given the other person a chance to speak.
9. And speaking of fact, before you start causing shit, make sure you know both sides of the story. It's wrong to make someone look/feel bad when they've done nothing wrong. Don't just jump to conclusions.
10. Try not to burn bridges. I understand that in some situations you really have no choice but to do so, but if this is a little thing don't do it. I'm not saying you should talk to them, but don't just tell them to go fall off a bridge and never look your way again. Creating enemies is never a good idea; I don't care who you are.
11. Don't talk down to them. Even if you are smarter, you should try to put yourself on their level. Maybe they'll understand the issue better. Please, don't make your goal be to make them feel stupid.
13. Always be honest, and remember: Forgiveness is the best policy.