In all likelihood, your divorce will be remembered as one of the most painful and difficult times in your child's life. It is a massive psychological trauma that can have many unwanted emotional side effects and affect every aspect of their lives - at home and at school. With that said, there is no doubt that you want the best for your child, so here are a few things that you might be able to do to ease the process and make things easier.
Don't argue in front of your kids. This kind of negative behavior will only create more confusion and stress. This includes speaking badly about your ex-spouse and the all-to-common, and frequently unintentional, tendency for parents to make children choose sides in the divorce battle.
Another common tendency is for parents to make children into confidantes. This arises from a desire to be close to the child as well as an overwhelming need to talk about the situation, especially when appropriate therapy is not in place. This does nothing but harm the child, creating confusion and feelings of resentment and an emotional weight that becomes difficult to bear.
In the midst of the divorce it is also common to make promises to children that you know (or suspect) will be impossible to keep. Promising vacations and visitation that have not been cleared with the other party or the attorneys, or promising to come to events that will fall on days when you do not have visitation rights. This will be particularly hard on you, but it is simply part of the divorce process. Whatever temporary positive feelings will result from the lie, the long-term mistrust will far outweigh it.
Finally, even if you are a once-a-month parent, do not give up your status as an authority figure. However infrequent, you are still the parent, and it's important to fight a tendency to surrender this role in favor of attempting to win the child's love through spoiling him or her. Do not allow your child to stay up late, become disrespectful, or act as if they run the house. This will only cause trouble down the road.
With all that said, it's important to remember that there are some proactive steps that you can take to make your child's life easier.
Tell your child's teacher about the divorce and attempt to get therapy. Your child will probably need it, particularly if grades begin to slip or behavioral issues emerge.
While you're at it, get therapy for yourself. You may need it to help you deal with your feelings and stress. You will need to be emotionally healthy if you hope to help your child to be emotionally healthy. This will also help you in keeping your problems away from your kids and not burdening them with your emotional baggage.
Finally, but foremost, always remember to keep the needs of your child before your own needs. Act as a unified front with your ex, even if you are no longer on speaking terms. Define a plan for your parenting that will address your child's needs and also (if possible) allow equal access to the children. This will help with the most important aspect of parenting, which is staying involved.