Contact witnesses who can support your story. Witnesses may appear in person at the hearing or supply a signed and dated written statement. If an important witness doesn't want to get involved, you can ask the court to subpoena them to appear. If the case is highly contentious or centres on technical matters, you may find it valuable to get an independent expert's written opinion. In a building matter, for example, you could get an assessment of the work by another reputable builder.
Relevant photos can also be useful.
If you and the respondent come to an agreement before the case is heard, you should put the agreement in writing and both sign it, and let the registrar know as soon as possible. If you need further help, discuss the matter with the court staff. The Ministry of Consumer Affairs has booklets and sells a video on disputes tribunals. The Department for Courts has also made a video, which can be viewed at district courts. The hearing Hearings usually last an hour or a bit more.