I think you should know, in your gut feelings, whether or not he is cheating on you. If you have any doubt on his worthiness, which it appears you do, I would hold off getting married to him. Your question is not the basis for a good start of a marriage.
In response to your question: You go through his wallet; you check the telephone bill for numbers called; you go through his car glove box and also his car, checking under the seats, in the trunk etc.
You check the pockets of his pants, shirts and coats. In other words, you play detective. You also need to be sensitive to changes in him. For example, does he no longer want to have sex with you? Is he buying sexier underwear? Does he have more overtime at work then he did before?
I don't understand why you are thinking of marrying a person that you don't even trust. If you are not sure whether he is worth marrying or not, then why to marry him on the first place? You should only marry a guy, whom you can trust blindly. Okay, I admit that guys can not be trusted blindly, but at least he must seem to be trustworthy to you when you decide to marry him.
If you really want the truth and are willing to do anything to find it out, you might want to check out www.CignalSpy.com - They have some pretty interesting services such as cell phone GPS tracking and text message / phone calls monitoring. Worked for me, could work for you too.
Sometimes when people cheat..they act strange. I'm not sure how they really act because I've never seen it happen. Sometimes they'll say they're going to work or someplace....and end up somewhere else.
Check out www.whataretheydoingonline.com they were able to help me