My brother-in-law was into it for a while, and I checked it out pretty seriously. Single Action Shooting Society (SASS) is the biggest. Someone already posted a link to their website. They are all about the shooting and the outfits they wear range from drug store cowboy to authentic old west attire. It's almost anything goes.
A rifle, two revolvers, and a shotgun will run you a few bucks - I figured $2500 minimum if purchased new. At many shoots, there are always people willing to lend guns to newcomers wanting to try it out. I'd suggest downloading their rule book so you can see what guns are legal in what combinations in the different "classes" or categories of shooters.
There is also a group called NCOWS - National Congress of Old West Shooters. It's a much smaller group and their focus is more on authenticity - in dress, camp, and guns. Much more like reenacting or even the old muzzle loader rendezvous crowd. IIRC you can get by with as few as 2 guns in some categories rather than the four required in SASS events.
Cimarron Firearms and Taylor & Co are two good places to search guns, although you can find less expensive.
www.taylorsfirearms.com/http://www.cimarron-firearms.com/The Cimarron website currently has a video about The End of the Trail - SASS's annual national championship gathering and matches.
I never really got into it, although I did shoot a couple of matches with my brother-in-law using his guns. It was fun.
That's about all my memory has to offer. The internet is your friend on this one - there are a ton of websites with good information for you.