The workflow with REST API from Unity App is exactly the same as from any other framework or without it. The UI has nothing to do with the REST API, you should implement it on your own.
If you specify the problem in more details, like what have you already tried and what not worked as expected, I think we’ll be able to help you more.
As to the documentation, the task to update it is already created and is in progress, the task ID is BKNDLSS-13014.
This means that the request is redirected - and this is expected. Along with this code you receive a header named ‘Location’, which contains the URL to which you should be redirected. In your case this is the URL to Facebook authentication service, if follow it you’ll see a login page where you should enter your Facebook login and password. In response you’ll receive a BackendlessUser.
Unity3D doesnt have a WebView, so what we can do is open url on user browser where user can get authenticated, however then there is no way to get information back from browser instance.
Unfortunately, we can’t help you further since we don’t officially support Unity yet and thus don’t know what it can suggest in order to take advantage of our REST API.
Looks like ill have to use a 3rd party web view for this purpose.
Thanks for your help, i was able to do both FB and Twitter, and will post a seperate thread for Google+