If you suspect that your girlfriend is cheating, you face an uphill battle. For starters, you don't yet have proof, and there's the possibility that she could turn the argument around on you for being jealous and lacking trust. But what if your suspicions are legitimate; how do you go about the dubious, unenviable process of confirming them?
One of the most surefire ways to track her behavior is by checking her phone. Many other suspicious behavior can be whitewashed with a clever, well worded spin, but the phone record doesn't lie. Look for high usage to strange numbers during blocks of time when you know you weren't with her. Texts are even more blatant and incriminating. If she's savvy and has deleted the damning evidence, try to find a way to check her bill if she happens to leave it open and around.
If you have yet to openly disclose your suspicions and are wary that snooping around her phone will negate any ground you have to stand on, then set a trap. One way is to send a romantic card to her work, unsigned. If she's cheating, she'll think it's from her new beau and won't say anything. If she's faithful, she'll either thank you for it, or simply wonder aloud who sent it.
Having several eyes and ears out there can be an effective, noninvasive way of learning about her comings and goings. Mutual friends work the best, since she too will trust them and perhaps let her guard down in public. The friends don't have to be de facto private investigators, but ask them to keep their eyes open. Odds are, your girlfriend will eventually slip up.
Her email and computer records will usually reveal a lot about her recent activity. This investigating may take some cleverness on your part, as it could be seen as an invasion of privacy. The key is to not act suspicious; just say your computer's broken and you wish to borrow hers really fast. Or, failing that, you can always opt for subtle, harmless keystroke software that tracks email addresses and such.