I’m going to update the documentation about delegated authentication soon, but I can give you some pointers right here.
First you need to open a browser session to discourse.site/user-api-key/new with the following parameters:
scopes: 'notifications,session_info,one_time_password',
client_id: YOUR_APP_CLIENT_ID,
nonce: GENERATED_NONCE,
auth_redirect: YOUR_APP_URL_SCHEME,
application_name: YOUR_APP_NAME,
push_url: PUSH_URL (if you are going to send PNs from Discourse to your app),
public_key: PUBLIC_KEY (generated in your app)
You can have a look at the implementation of our DiscourseMobile app for details on the above but the main idea is that your app will launch a browser screen to the URL above, asking the user to authenticate to the Discourse site and authorize your app access to it. Once user authorizes access, Discourse will redirect to YOUR_APP_URL_SCHEME?payload= with an encrypted payload. You’ll need to set up your app to decrypt the payload and store the authToken. In iOS, you should use Apple Developer Documentation (I don’t know if there is an Android equivalent).
Your authToken can make API requests limited by the scopes requested initially, for a full list of scopes, please look under allow user api key scopes in site settings.
The one_time_password scope allows the authToken to make a request for a one-time-password. The endpoint for this is /user-api-key/otp with the parameters auth_redirect, application_name and public_key.
I will write a proper documentation shortly, but this should help you get started.