How do you tell your girlfriend that you're gay?

Unfortunately this is something that will hurt his girlfriend whatever he says or does, and he really needs to be honest as lying or keeping it from her will hurt her more in the long term. He needs to sit her down and tell her how sorry he is and that is isn't a reflection on her, but he needs to be true to himself. Yes it will hurt but if he's honest she will eventually respect the fact he told her with sympathy and she will move on. It's not an easy situation but it will sort itself out with time and both Matt and his girl will move on.