The Disputes Tribunal was established by the Disputes Tribunals Act 1988, and its processes governed by Disputes Tribunals Rules 1989. You may know it as the ‘small claims court’. You can find copies of Acts and Rules at legislation.govt.nz.
Timeframes for any court or tribunal are subject to all sorts of factors and no estimate can be given with any real certainty. However, in an attempt to give a very rough and general estimate, you may expect to have your case resolved or otherwise determined within 3 months of a claim form being filed.