You can log in to the API explorer site to request access to APIs. As a logged in user you can set up and manage your API access credentials.
To register you need a RealMe login. If you've created a RealMe login somewhere else, you can use it here too.
RealMe is a service from the New Zealand government and New Zealand Post that includes a single login, letting you use one username and password to access a wide range of services online.
You can manage your RealMe account here.
The first time you log in to API explorer you will need to set up your user profile with contact details. All communications, including subscription approval notifications, will be sent to the email address entered here.