They go to the starter areas to greet new people that request them. They show them a few things about the game and actions and then turn them loose upon the world.
I don't know if any are being accepted right now since we're back in beta, though. The best way to find out would probably be to send a Help ticket addressed to Jade with your questions.
Yeah, there's not many people joining the world these days so I don't think Jade is letting people join. We currently have roughly 198 Greeters, including me.
Jade has the list. As Little Miss Giggles said, submit a bug report addressed to Jade if you're interested in being a Greeter. See here for this information.
I remember hassling my greeter, " are you a bot? ", " what is 3 x 4? ", " are you a bot? ". Then when they convinced me they were human, i fled, all embarressed of my noobity!