I'm so sorry you are going through this. I have seen and heard of many divorces. The advice I would give you is this:
While you can do some things yourself, you will be best served getting an attorney. What may seem and start as a simple divorce soon becomes something that is not so simple. Even when there is little to nothing acquired during the marriage sometimes one spouse will deny the other the very air they breathe while going through the divorce process.
Don't be deceived any longer about how ugly divorce can be. Prepare for the worse while hoping for the best. My husband divorced in 2004, walked away with only the clothes on his back. She got the kid, the house, a portion of his 401K and everything else in the house. Seems simple right but it was still a messy divorce. Lawyer's were required.
Another girlfriend filed for divorce, tried doing it through a mediator but he wanted alimony and for her to continue to pay for the house. She ended up getting an attorney just to move the process forward.
Try not to dwell on the other woman and put yourself down. Concentrate on envisioning life after him for yourself and your children. It is fine to also include in that vision a future with a husband that will be faithful and loving to you and your children. The other woman doesn't matter, you do.
No matter how angry or hurt you may be with this man, he is the father of your children and because they get part of their identity with you, you must treat him with dignity and respect and require the same from him. Don't allow your children to be pawns of divorce. Be well and encourage yourselff through this process.