You can use a Fencing Notice if you've already tried and failed to reach an agreement with your neighbour.
The Fencing Notice has to specify the boundary along which work is to be done, the nature of the work (e.g. building a new fence or repairing an existing one, and what it will look like) and the materials to be used. The notice has to state an estimate of the cost of the work, and how those costs are to be shared (if you propose that they aren't shared equally).
It must also tell your neighbour that they have 21 days to object (see the next question), and that if they don’t object within this period they will be deemed to have consented to the work.
You can download a sample Fencing Notice from the NZ Legislation website.