There's not really any formal process, though I think it depends on which reviewer you're looking at. I liked Lupa's videos, noted that a) she did not have a title cardist and b) I thought it'd be fun to do.
So I just asked her. XD I sent her a message on tgwtg with a link to my gallery and asked if she were interested. Turns out she was. And that's about it. Like I said, I think it depends on who it is, but I know that both me and *Masterthecreater (Linkara's cardist) pretty much just said "hey there reviewer person, would you fancy an artist?"
The tgwtg site is how I got a hold of Lupa. I just made an account and sent her a message via tgwtg. I honestly didn't even think she'd respond. XD If your person is on facebook or twitter a lot that might be a better option, but I figure all you can do is send a message and hope for the best. Sometimes if you ask, reviewers will set out lines for you--tweeting that you're up for title carding if anyone's interested or something like that. Oh! Or if you know a guy who knows a guy. *AndrewDickman pretty much knows everybody. He's busy a lot though so he might be just as hard to get a hold of as a tgwtg producer. >.> Actually between ~TheButterfly, *Masterthecreater, ~Berlin-Poe, *VenGethenian, *AndrewDickman, ~Mochita-chan, and I, we're probably 1 to 2 degrees of separation from nearly everyone on that site. XD Fewer if you count the other title cardists, I guess, but I don't know the other ones.