You can purchase a new bike from a bike shop, or purchase a secondhand bike through an auction website such as Trade Me or Facebook Marketplace.
Motorcycles and Mopeds are registered with the New Zealand Transport Agency and will require annual registration and a change of ownership notification the same as for buying or selling a car. You will also require a drivers licence to ride these, find out more here.
Low powered Electric scooters or e-scooters do not require registration or a drivers licence.