Whenever someone asks how can they tell if their mate is cheating I usually tell them to trust their instincts. Sure you could hire someone to follow them, snoop through emails, and cell phone bills....etc The bottom line reason we "suspect" cheating is due to a change in our partner's behavior towards us. Usually these are changes which we dislike. Basically what we are looking for is an "explanation" for the change in their behavior. Learning they are cheating simply gives us the "aha!" that explains it moment....etc
However lets say it turns out they aren't cheating and the behavior remains. My guess is you're not going to suddenly jump for joy.
You are responsible for your own happiness and if you aren't happy in your relationship then you have to decide whether to stay or not.
Too many people believe being "unhappy" is not a "good enough reason" to end a relationship. It's as though they actually "need" their partner to cheat on them or abuse them in some way to "justify" ending the relationship. Since we cannot "change" another person we are left with communicating our feelings and if they aren't on the same page as us we have to make a decision.
If something doesn't "feel right" to you then it's probably "not right for you". Trust your instincts. Unless you are paranoid by nature odds are you are not getting what you need to feel secure in the relationship. (If you don't trust your mate that is a good enough reason to move on in my opinion.) Best of luck!