Agree to disagree, but never in front of your children.
You and your spouse might be angry enough to spit nails at one another, but if for no other reason (and what better reason is there?) than love of your children, you should have a discussion right at the outset and reach certain agreements. Agree not to argue in front of the children. They're stressed enough! They don't need raised voices, cold shoulders, or out and out brawls to add to the turmoil they are already feeling. Agree to be respectful to one another in the presence of your children. Agree to be flexible with visitation arrangements. Agree that both parents can attend extracurricular activities of the children.
Attend a seminar for divorcing parents.
Many jurisdictions require this step for parties going through a divorce. Attend a seminar to make you aware of just what and how your children might be thinking as you go through the process of the divorce. This awareness will help you communicate better with them about their own feelings as they begin getting into a schedule of living in more than one house and only being able to see one parent at a time.
Hold your tongue!
Do not discuss your divorce case WITH OR IN THE PRESENCE OF your children. Do not discuss your feelings about what YOU are going through. It's certainly fine to discuss the children's feelings, if they wish, but do not discuss yours. Do not tell them what a "piece of work" (or other term of endearment) the other parent is. Never tell them they should not love or respect the other parent. Be sure your family members (parents, siblings, etc.) also refrain from making derogatory comments about the other parent to or in front of the children.
Make sure your children understand that your separation/divorce is NOT their fault. Children frequently blame themselves for their parents' separation.
Tell your children often that mom AND dad both still love them very much and that they are still the most important people in both your lives. And make sure they understand that it is okay with you for them to still love the other parent, sometimes they need to hear this from you.
Make sure they know that they will still have time with you, even if you are no longer all living in the same household. Be sure to express how much you are looking forward to their next visit.
Even though you are not all living under the same roof, try to maintain as many family traditions as possible.
Stability is key - make sure your children feel secure in either home, that they will be allowed to maintain their lives outside of home - sports, arts, school, church - and that they will have quality time with each parent.
No grilling!! Your children are not meat!!
Too many parties in divorce cases want to make their children into witnesses or, worse, spies. Do NOT ask the children questions like these: Did he say anything about me? Did he have his girlfriend there? Did he drink alcohol while you were there? What did he feed you? Who came over? Who did you see? Did he get any calls? This type of behavior tears kids apart. They want to please you and so might "help," but then they are eaten up with guilt at spying on the other parent. Don't put your kids in this position!