Depends on the tournament. I've done a bunch of tourneys where we'll do a charity event and people can come hit with pros, typically the day before the tournament starts/last day of qualies.
There are also a few tournaments that will do an event in between matches. Every year at the Legg Mason, for ex, Wayne Brian will MC an event in between the night matches where they'll bring people out on court to play against Roddick or Blake with the proceeds going to charity. All the volunteers get a goodie bag and have their picture taken. Pretty sweet.
The main requirement is generally to look stupid and wear tennis shoes.