Dealing with children in divorce means thinking like a child while acting like an adult..

[edit] Steps

Try to see your ex through their eyes -- as their mother/father.
Remember that you will probably have to deal with your ex for the rest of their dependent lives. Try to make the best of it.
Envision a happy life and healthy future for them.
Think of the benefits of the divorce -- such as parents being happier apart and less fighting.
Talk with your ex about continuing toward the original goals you shared in having children.
Broach the divorce to the children together, if your ex is willing.
Encourage them to tell you how they feel about it.
Do not take their anger personally.
Try to maintain discipline using the same rules and structure as prior to the divorce, unless those rules and structures were a cause for the divorce.
Spoil them with attention, not things.

[edit] Tips

Accept your ex's limitations.
Expect bad behavior from your children.
Remember to tell your children that you love them and always will, even when you're angry.
Scientific studies show that the #1 cause of maladjusted kids is conflict between the parents. Even if your marital/romantic relationship has ended, you need to be partners in parenting for the sake of the children both of you love.

Don't badmouth your ex in front of your children
If you do badmouth your ex, apologize to them
Don't use your children to get back at your ex; your children love both of you the same, using them against your ex, is like having them choose which parent they love the most.
Most of the time, in divorce situations, somehow the children are overlooked, almost forgotten. The adults are so wrapped up in who gets what, that they don't realize how bad they are hurting their child(ren). Be sure to explain to your child, that they are still loved by both of you, and don't fight or argue in front of them. Be an adult in this situation, and be strong for your child.