Divorce is difficult for children. How you break the news can impact how they deal with it.
As parents, we have to do a lot of things that aren't pleasant, telling your children that you are no longer going to be married to their mother or father is one of those things. Do not tell them apart. It is important that you both be there to explain to the kids what is going on and why. The main thing you will want to do is reassure the kids that the divorce is not their fault. Be sure to tell them that you and their other parent still love them, but sometimes married people just can't stay together.
There is no easy way to tell a child that you are divorcing. Being honest with them is essential. They need to understand that you and their other parent are not divorcing them. Kids take things to heart so easily, even today. Some will honestly believe that they did something to cause the breakup and will promise to do anything better just to keep you together. These are the kids that need that extra reassurance that it is not their fault.
You will also have the kid(s) that will blame one of you. If you had done this better, or that better, the other parent would have stayed. They are kids, they don't understand and it tends to make them feel better to have someone to blame. That is understandable. That is why it is important that both parents tell them that the divorce is not the fault of either parent. While being honest with them is important, they don't need to know that you are divorcing because one of you cheated. You both need to take responsibility and tell them that sometimes you just can't live together anymore.
No matter what the reasons are for your divorcing, the main thing you should both focus on is making sure that the kids understand that you will both be there for them and you still love them. That it isn't their fault and that as parents you equally share the blame for the divorce.
In this day and age, divorce is not uncommon. Children hear from their friends about it and why it happens. Expect questions and give them answers. Let them know that they can talk to either of you at any time with any concerns they may have. They will want to know who they will be living with, when they will get to see the other parent and probably a dozen more questions. Before you talk to the kids, talk things out with the prospective ex and work out the answers to these type questions. Also expect the kid that will try to play both sides against each other. They have probably heard about this from their friends and think that they can get away with it. Be strong and stand together, even though you are divorcing.
Try not to argue in front of the kids while working out the details. Yelling and screaming at each other frightens the kids, makes them aware of the situation more and tends to lead them to believe it's their fault. Be adults, show your kids that despite the fact that you can't live together, that you will be there for them, always.