Dig up as much evidence as possible in discovery before your hearing. Discovery is the part of a civil lawsuit where each party uncovers evidence that might have some bearing on the case. Exactly what discovery techniques are available to you--and how far in advance of your hearing you have to roll them out--depends largely upon the requirements of your state's rules of civil procedure. For the do-it-yourself-er, the simplest discovery techniques tend to be interrogatories--written questions the other side must answer--and document production requests. In document production requests, you can ask the other side to produce specific documents or entire categories of documents, such as bank or credit card statements, for a certain time period. These don't have to be written in some complex form; just ask the question or ask for the document in writing and make it clear that you're doing it under your state's interrogatory or document production request rule. If you don't want to do this or feel like you can't, don't despair; many lawyers do little or no discovery, so you won't necessarily come up short.
Review the law applicable to the issues which you will be hearing. If you're fighting an alimony case, read your state's alimony statute; if you're fighting property division, read the statutes on property division. These statutes will set forth the specific law on what you have to show--or prevent the other side from showing--in order to prevail. Statutory law isn't hard to find; these days, most legislatures have every statute on the books available for free on the Internet. Go to your legislature's home page, look for something like "general statutes" or "code of laws" and page through the table of contents until you find the section on family law. This may be expressed as something like "Family Law" or "Domestic Relations."
Review all of the evidence you managed to get your hands on and any applicable statutes a day or two before the hearing. You'll want everything to be fresh and clear in your mind so that you'll have no trouble accessing it when something comes up at trial. Organize your materials so that if you need to whip something out, you'll be able to find it quickly.
Develop a list of points you need to make in your case and practice your own testimony. Develop a list of questions for all of your own witnesses, and map out areas of cross-examination for the other side's witnesses. Make a checklist of points you want to score at trial, and mark them off as you make each one.