Question is in the title. How do you start it?

You rescue him from Black Mountain - there should be a radio broadcast from Super Mutants which mentions him. Be warned, if you do rescue him, you may get the maintenance perk and he's a damn good shot with the Hunting Revolver (I think that's what it is) but he gripes, complains, pisses and moans a lot about his bad knees, cataracts, etc. I'm thinking of finding someone else because I'm getting tired of it.

Yeah, I've already got him as a companion, it just hasn't activated (or at least I don't think it has) the option to do the rest of his story line (either becoming a gunslinger again or a better mechanic, the latter of which I'm actually interested in).

Oh. That part hasn't activated for me, either. I didn't even know he had a personal quest.

Every follower has a personal quest that triggers based upon conversations and actions taken. Raul's conversations seem to trigger from NCR military officials. I got one convo at camp McCarran (sorry, don't remember who it was, but it was one of the first recon team in the tents outside). Another triggered at Forlorn Hope. I hope that helps a bit.