Yes you do go through Twist Mountain; it happens after you beat the main story line (i.e. the Elite 4).
You can access Twist Moutain via the Clay Tunnel in Driftviel City.
Marriland's guide on Clay Tunnel
Incidentally, Twist Mountain is where you find Regigigas, but you need Regice Regirock and Registeel to be able to capture him.