The Japanese working holiday is the most well established working holiday schemes in Asia. The Japanese have put together some info on the Japanese embassy, Wellington website.
Date agreement signed: 1985 
Agreement signed by: TBC
Number of visas available for New Zealanders: Unlimited
Average annual quota used: TBC
Processing time: TBC
Visa length: 1 year 
Visa fee: TBC
Age requirement: 18-30 inclusive 
Difficulty to get visa: 3/10 – pretty easy.
Time allowed before entry: 12 Months
Can apply outside of NZ: No – are required to be an NZ resident at the time of application. You can apply by post, but will be required to collect your passport with visa in person in Auckland or Wellington. 
Extra immigration steps: Yes, two things to be aware of:
1. Once you’ve found a place to live you are required to register your address at an immigration office within 14 days (Best to take a Japanese friend if you’re still working on your Japanese!). The Jury is still out about what happens if you don’t settle down long enough in one place to do this.
2. If you wish to leave Japan and return again on the working holiday visa you MUST fill out a reentrant card and give this to border control BEFORE you leave.
Work/Study restrictions: TBC
Full guide coming in Jan 2017.