In case you want to keep the relationship and care about his state of mind of the second half, start with "preparing the ground". Choose a convenient time to talk and secluded place to no one will disturb, start a conversation. Say, for example, that your life together is very valuable for you, and you are afraid to destroy it. Add that all human beings are fallible, and you fully repent of misconduct.
Do not start the second half of his accusations of various sins, actions and failures that prompted you to treason. Reserving these arguments for later, if at all needed. It is quite possible you just do not want to hear any more. Do not panic if people hear your confession, he immediately slams the door and leave. Do not run after him, not to humiliate, crawling on his knees. People need time to reflect on what happened, understand, accept, "digest" it. Typically, cooled down, a person is able to return to full-fledged dialogue.
Explain that it was not love, that you are mistaken, emotion prevailed over reason. Now that the conversation will have a calm nature, explain the reasons that prompted you to take this step. Without rancor, bitterness tell that you feel very lonely, abandoned, that the partner gave you enough time. Tell us what you're looking for in another person, for example: emotional support, companionship, friendship, etc. Promise that you will try not to repeat their past mistakes in exchange for more attention to you.