The thing about trust is that once it has been lost from your relationship, there is very little left. Trust and honesty are the very basics of any relationship and abusing one will cause a quick downward spiral before you have even had a chance to think about. The good news is that trust that be rebuilt. The bad news is that it will take a long time and a lot of effort so it is worth thinking twice about betraying your partner before you go ahead and do it.
The first thing that you must do to rebuild the trust within your partnership is to actually admit that something has happened to break that trust. If it was a lie on your part that caused the breakdown of trust, admit that you lied and promise that it will never happen again. If you cheated on your partner and your partner is suspecting, admit it and try to rebuild the partnership. If the doubt is already in your partners mind, there is a good chance that the trust has already been broken anyway so your best bet is to just admit that something went wrong.
Secondary to being honest about the trust issues with your lover, you must also take a good amount of time to sit down and actually figure out why you did what you did. Are you and your partner not having sex anymore? This can lead many people to search for sexual relations elsewhere. If you have lied about going somewhere then perhaps you are not being given the freedom that you need within the relationship. The only way to really fix the problem is to first figure out where it actually went wrong.