As with all GTA missions you'll be given a yellow GPS marker with a route to follow, follow these routes to your destinations.
Upon starting The Lost And The Damned DLC you are on your bike with Billy on the back, you'll be required to drive back to the Clubhouse, upon arriving at the clubhouse you'll find out that Billy's bike has been taken and you must go get it back.
Again on the bike with Billy drive to the chopshop and once there you'll be told where to go for Billy's bike. When you arrive there will be 6-8 enemies to kill once these have been taken care of billy will run back and get on his bike and the achievement will be yours.
Here's a video walkthrough with the cutscenes removed.