I've started doing a little freelance web work and I've got to build a site for a client. The client doesn't currently have a hosting service, so either I or they are going to have to set it up. Traditionally, how does this work out? Do I set it up and then transfer ownership to them when I'm done? Do I leave it to them to set it up? If they're going to be paying for the hosting directly, does that affect anything?

Basically, I'm brand new at all this and any and all advice on how to handle hosting would be greatly appreciated.