Sorry you are here Healingsought. If you haven't check out the "healing library" in the upper left side of the site. It has a lot of great information.
Please remember to take care of yourself, eat and drink when you can. This is tough and it takes along time to recover from infidelity but you will get through it. If you haven't please go get tested for STD's asap. Your wayward boyfriend (WBF) needs to get tested as well. Is the Affair (A) actually over? Whether you check or not he should give you full transparency, i.e., passwords and access to all email accounts, facebook, cell phone access etc. He also needs to put NC or no contact in place with the affair partner (AP).
To answer your question you begin to move forward by focusing on you. You can't change your WBF. He has to do that work on his own. He has shown you who he is prior to you getting married. Now he gets to show you if he is truly capable of changing himself or not. Right now his words and some of his actions seem to point that way but it's consistent action of a very extended period of time that you want to see. It's said that it can take 2 to 5 years to recover from infidelity. Please take care of yourself. Sit back and ask yourself what do YOU want. Seriously put some thought into this and then go about doing something that you wanted to do while your WBF works through his issues. Read up on the 180 and detachment in the healing library.
Again sorry you are here but there is a ton of knowledge here for you. I wish you the best.