Folkstyle is what you do during the kids wrestling season and what you do in high school and college. You know the point system so I won't go into it.
Freestyle is in essense similar in that you can shoot to take a guy down. However the way you get a guy down is scored differently. It's all based on amplitude. If you just take him down, that's 1, expose his back while taking him down is 3, and drop him on his head (that's not really it's terminology, just making it easy to understand) is 5, maybe even 6.
Greco (Rulon Gardner's preference) is all about throwing a guy. You can't touch his legs at all. The point system is the same.
Once you get an opponent on the mat, you can score points for back exposure, 2 pts., hold for a five count is 1 extra.
The biggest difference between the Olympic styles and folkstyle is that folkstyle is punitive for aggressiveness via slamming an opponent and the Olympic styles are not. The best analogy I can give you is if you slam a guy on his skull in folkstyle, shame on you. If you slam a guy on his skull in freestyle/greco, shame on him for letting you do it.
coach gibson