I am not an attorney, but here are a few of the things I have learned about representing yourself in court...
You are bound to make mistakes if you represent yourself. One way to minimize that is to go and spend some time in divorce court as often as you can to see what goes on there.
Here are some very basic rules for presenting yourself in court, whether you have an attorney or not. Some were related to me by my attorney, others are from experience:
First and foremost, NEVER, NEVER, NEVER interrupt or argue with the Judge! You can respectfully disagree with him, but be careful and tactful about it. His decision is final for all practical purposes, so you DON'T want to tick him off!
Never interrupt the opposing party. Wait your turn. Don't use gestures, facial expressions, or other distractions when the opposing party lies. You expect them to lie, that is why you are proving everything. If they are saying that you are violent or a villain with a short temper, you need to show otherwise instead of taking the bait. Attorneys, especially, use inflammatory language and gross exaggerations. Expect it, and stay calm. Judges are used to the exaggerations, and will carefully watch your reactions to form their own opinions.
Write down exactly what you want to say in advance. You can count on being nervous and forgetting half of what you want to say. Practice this and make sure it takes less than 4 minutes. Don't be afraid to read your statement to the judge. He understands that you are nervous.
Be precise and succinct. Don't say "she has denied visitation many times." Say "she denied visitation on these dates, resulting in the loss of X days of time with my children and causing serious detriment to the healthy relationship between father and child". (See Tips on Keeping Documentation). A good way of organizing your statements is to say what occurred, what resulted, and how that helped or hurt the children. Remember, the children are the Judge's focus in divorce court. Your "rights" don't mean squat to him.
You can't win a he says, she says battle. Make no allegations or accusations you can't back up with hard evidence. Witnesses are OK, but hard evidence (such as school records, medical records, written correspondence, etc.) is much better. (See Gaining Access to Your Child's Report Cards and Accessing Your Child's Medical Records). The only exception to this is when they make false allegations, which you must fight whether you have evidence or not.
While the other side is presenting their case, keep a list of points/topics that they bring up that aren't already a part of your case. Then make sure to ADD them into your case somewhere along the line. If you don't respond or deny an allegation, the other side will argue (and the Judge will have no choice but to agree) that their accusation/evidence was not even disputed. I have used the argument in court before that "This was a blatant attempt by the opposition to distract the court from the true focus of this hearing, which is the children [in this case it was the children's education], and I will not waste time on this issue other than to say the allegation is completely untrue." (At the time I made that response I was being represented by an attorney. He liked that argument and included it in his own statements).
Remember that there is a gender bias and many fathers do not win the first time through the courts. Bide your time, save your money, and don't jump before you are ready. If you don't have the hard evidence you need to win, then you probably are wasting your time and money. Waiting until you are ready is tough, but better for both you and the kids than a prolonged court battle with many repeat engagements.
All of this will be moot if you don't know what you are doing. You need to read the applicable statutes, court rules, and case histories. You need to know when to object when the opposing attorney tries to introduce hearsay as evidence, or violates other rules of evidence. Spend as much time as possible researching in the law library and observing other cases. This will not make you an attorney, but will help you avoid some of the most common and blatant errors. If you forget to provide a bench copy of your affidavit, or fail to comply with all of the rules of evidence, for example, then the judge probably will not be willing to look at it in the courtroom. Simple misunderstandings like that are common in pro se cases, and can cost you the case no matter how much evidence you have or how well-founded your case is.
Shave, get a hair cut, and wear presentable clothing! For men this means a business suit. For women, you need to be businesslike and presentable. Think of a bank manager. I once had a judge ask me who I was representing when I approached the bench. He just assumed I was an attorney. By dressing appropriately, you both get respect and show respect for the court and the judge. You want to differentiate yourselves from the real scumbags these judges have to deal with on a daily basis.
Good luck! I hope these help. I still advise that you find the money somehow to get a good attorney. An attorney doesn't guarantee success, but it greatly reduces the likelihood of failure. I'm sure many others here will agree with me.