If this is about cheating, the thing to know is some people cheat after years in a relationship, because things have gotten off track and instead of working it through with their significant other they fall for the attentions of another and cheat. When these people are caught, they either want to keep the primary relationship, in which case they will be very remorseful and want to talk and work things through, I think you can gain trust back in this case; or, they were looking for a way to end things, and this might be the beginning of the end. Then, there is the cheater who cheats just because he will always cheat (I use he here, but there are women like this too). If he just did it and has no complaints about your relationship, thinks there is nothing to work on, that is a really bad sign, he is probably not trust worthy. You will never gain the trust back if the cheating party will not answer your questions and do whatever you need to trust him again.
If this is about lying, lying is REALLY BAD. This many times is coupled with cheating.
If this is about physical abuse, be really careful, is this the first time he has physically abused you? Is he very controlling in general? Very possessive? All very bad signs, you should not be with someone with these characteristics.
If this is about him not being there for you when you needed him, if you both are very young, this might be a learning process, and if he understands where he let you down, you could definetly gain the trust back.
So many possibilities.