Question: how to use rgc to play dota?
Answer: Start RGC.
Login.
Start Warcraft by clicking the "Warcraft" button at the lower left of the RGC Interface.
 @ ... 
Going back to the RGC Interface, choose your game mode to join (AP,CM...)
Sign in and wait for the game to be hosted (needs 10 players who signup for RGC host a Game)