Twitter is just for quick 1-liners. To be honest, I'm not sure how it would fit into a detailing business. I could see big corporations using it, like Air Canada, where they could tweet 1-liners like "Seat sale from Toronto to Zurich !". They would also be big enough to have enough people "following" their tweets.
Facebook is awesome, start by creating a page for your business (FB has tutorials on how to do that, or feel free to private message me if you have problems). FB lets you send group messages to your fans, lets you create photo albums, blah blah blah. Basically think of a normal personal Facebook profile, but just for your business. You can also get into advertising with FB, not sure if you want that or not.
YouTube would obviously be for videos. You can do "how-to" videos if you want, or just a video of how you detail. Important thing to note is to keep the videos on the shorter side, most folks aren't going to sit there and watch a 20 minute video, let alone wait for it to load.