Starting a new relationship is always difficult, but a some point you're going to have to determine whether you plan to be monogamous or not. If you haven't had the conversation, having it will save you from wasting your time, but if you have, and he says he'll be faithful, educate yourself on signs that may point to the contrary. While we all have a heightened sense of awareness when it comes to people we care about, knowing when something is really amiss is the best way to put a stop to it before it goes too far.
Be alert when he says he has a sudden need for privacy. If your partner has started changing the password on his computer or has started opening extra email accounts, it may be time to take a closer look. Gradual separation from you can begin on the electronic front, for example, buying another cell phone or staying up late at night to "play video games" or "get some work done" could mean that he's checking out dating sites or chatting with a "friend." Also, keeping his phone bills, credit card bills and bank statements away from you, could mean purchases that you aren't meant to see.
Be curious if your sex life changes. Depending on the amount of time you've been together, you know each other's patterns when it comes to sex, but be aware of sudden changes. Your partner's desire for sex decreases suddenly, which could indicate that he's been too busy elsewhere to perform adequately with you. If he begins to have unusual or kinky requests, he could be learning new things from someone else and either enjoys it, or it has sparked his desire to experiment. And while he's undressed, check his body for strange scratches or bruises.
Guilty behavior. If he is feeling guilty, chances are, he'll start being proactive about cleaning up his mistakes. This can show up as a sudden need to talk at strange times, and long winding conversations. This might be him trying to tell you "something" that he can't bring himself to say. Another sign is picking a fight where there is none, causing you to lash out and giving him a reason to continue his behavior. Transference is another sign of guilt. He begins to accuse you of cheating, and won't let the issue go.