They're pretty straightforward. I did my own divorce long before I went to law school, and had no problems. Every court is different, of course, but in my experience:
1. The judge takes your word for things, assuming everything is fair and equitable. Meaning, we didn't need to get an appraisal for the furniture or for my ex's guitars--we just decided that the bedroom set was worth the same as the musical instruments and went from there.
2. The court self-help center or library can't give you legal advice, or determine whether you've negotiated a fair agreement, but they can check to make sure you've filled everything out correctly. Use black ink or type (these days, you can usually get downloadable forms you can fill out right on your computer). Don't leave anything blank unless the instructions say so--at least put "n/a" (for instance, there was a section on my form asking what we were doing with our boats) so the judge knows you didn't accidentally skip anything. Make sure everything on your financial disclosure form is somehow accounted for on your property agreement.
3. If you deviate from state norms for custody, child support, or property division, be prepared to explain why. I got $25,000 more from the sale of our house than my ex did, because I provided the entire down payment and he agreed both at the time of the purchase and time of the divorce that I should recoup that. We did not have a written prenup/marital property agreement, but the judge just made sure we were both OK with the property division and that we understood we could consult a lawyer and that once this was final, we couldn't really go back.
4. Remember a lawyer is $200 an hour, and a skillet is $15. It may be worth hiring a lawyer if you have big disagreements over your children (it's hard to advocate on their/your own behalf when you're emotionally involved, and the stakes are much higher), but it is generally not worth it to fight over small personal property. Just about all of the property my ex and I owned had a logical owner--it either came pre-marriage (my dining room table), or was a gift from one side of the family or the other (our bedroom set was a wedding gift from my parents, so I kept it), or was obviously used by one of us and not the other (our respective cars, his guitar collection). We used rock-paper-scissors to determine who kept the small stuff, if we disagreed.
ProtoLawyer (the now-actual lawyer, this isn't legal advice, please don't take legal advice from some anonymous yahoo on the Internet)
Spouse (the political geek) * Stepdaughter (the artist) * and introducing...the Baby (um, he's a baby? He likes shiny things).