Whether you are a plaintiff (the person suing) or the defendant (person being sued), you need to back up your story with evidence. One of the best ways to prove your case is with letters or in-person testimony from eyewitnesses or expert witnesses. For more information, see Nolo's article Offering Witness Testimony in Small Claims Court. Depending on the facts of your case, you can also use photographs, advertisements falsely hyping a product or service, and written contracts to convince the judge you are right.
Before you go to court, you might want to learn some common (and perhaps even not-so-common) legal terms. Get Nolo's Plain-English Law Dictionary, now available as a free iPhone app (also compatible with iPod touch).