Go to https://developer.alfresco.com and sign up. When your account is approved, you can register your application. You must provide a callback URL and a scope. The callback URL is the part of your application that exchanges the authorization code for an access token (http://www.alfresco.com/mobile-auth-callback.html). The scope should always be set to public_api.
Once your application is approved, The Auth tab will show an API Key, and a Key Secret. These will be needed by your application for authorization.