Easiest to give you this link:
http://www.nssf.org/events/featurette/2012/0712.cfm The NSSF is a good resource.
The article is a short one, but describes "Three-Gun" very nicely.
You might also check out some of the other links w/in the article. Lots of info out there on this shooting sport.
BTW, I did quite a bit of training on a 3-gun course my son-in-law set up at his outdoor range. One of the two challenges or "obstacles" he used for the shotgun portion was to shoot through a locked wooden door. He taught me how to do that, and it was a fun course to navigate!
Also for a handgun, I prefer a revolver over a semi-auto. I've read there are competitions that are set up to allow revolvers. The additional challenge there is to do on-the-run, in-the-field reloads. My revolver only has 5 rounds, so at least one, possibly two reloads would be needed. I got pretty good with a speed loader.
It's a fun and exciting sport. If you go for it, I'm pretty sure you'll like it.