They get the show going with the bareback bronc riders. I personally think this is one of the best events. It's better than the bull riding. The horses are more lively and yet more contestants manage to stay on the entire 8 seconds, which means more of them actually get a score. Scoring is based on two factors: the animal's movements (how many times they buck, turn, etc.), and the cowboy's performance (how they sit, move, etc.). If they get bucked off, they don't get a score.
The guy in green is there to manage the animals after each contestant finishes his ride. They also help contestants get off their horses by riding up along side so the contestant can reach over and grab him around the hips in order to get off the horse safely.
Here we have what's called "Bulldogging" or steer wrestling. Two guys ride out of the chutes together, one on each side of a steer and one guy jumps off his horse, grabs the steer by his horns and wrestles him to the ground. Easy enough, right? This is the rodeo sport I'm thinking of taking up...
Bull riding...not for the faint of heart.
Wild cow milking. This falls in the non-traditional event category, but it's fun. It's fairly straight forward. First, rope a wild cow.
Second, milk said cow while your partner holds her still.
Third, run your bottle of milk to the judges.
There are more events, of course: barrel racing, calf-roping, wild horse racess, sadle bronc riding, etc. You'll just have to go check them out yourself. :)