With a user registration, it would function very similar to any other kind of form post that you would do. You should have some sort of registration endpoint within your API application that would create the user. You may have something like http://example.com/users/create where you would make an HTTP POST to via your app. You would pass in the parameters

{
  user: { 
    first_name: 'John',
    last_name: 'Doe',
    email: 'john.doe@example.com',
    password: '123456',
    password_confirmation: '123456'
  }
}

and your model would have the necessary validations to ensure password complexity, and email uniqueness. If the user is created, pass a successful response. Otherwise, you would respond with an error.

You would also need to provide an authenticate method for your user. In this example, we simply used devise to handle the user registration and authentication. While you could do something similar in an API only application, it might be a bit heavy. However, using the devise logic (not necessarily the views), will give you access to a lot of the built in functionality around locking out the user, confirmation signups, etc.

Depending on the architecture of your application, you can make the new user registration only available under the client portal. Also, if you are using some sort of role based authorization, make sure that you set the default access to a client role. 

Hope this helps!