The club buys or rents stones. They're probably about $8000 for a set of 4. A draw (game) needs 8 stones. They're about 40lbs each, the nice ones are granite from one small island off of Scotland (Ailsa Craig). I think they may make cheaper ones out of more standard granite, but who wants substandard stones?
My home curling club (Traverse City) currently rents ice time from a hockey rink. It's a huge pain in the ass. Skaters do a real number on the ice, gouging it up and everything. We start out a league night by the zamboni running over it for 20 minutes trying to make it as flat and smooth as he can. Then another 10 or 15 minutes of pebbling the ice... That is, curling isn't played on smooth ice, it is played on a rough surface created by essentially raining water onto it. The stones won't go anywhere otherwise.
In the next year or two we're going to have dedicated ice. A facility dedicated to curling, where the ice is always flat and ready to play. The stones are already out on the ice... Man, I can't wait.
I would recommend it to anybody who is remotely competitive. I would classify it as a "leisure sport", but, to be honest, if you're trying to get as much curling in as you can in the 2 hours that you have the ice, there isn't a ton of time to drink your beers. It's a really friendly/social game, and you can usually start without any special equipment.
There are clubs all over the country; even down south.
Hokie, it looks like Charlottesville may be the closest club to you... It's a haul, but we have members in our club to drive 2+ hours...
https://www.facebook.com/blueridgecurling/