Just like in bareback riding, the rider must ‘mark out' his horse meaning that both feet must be in position touching the horse forward of the break of the shoulders, on the first buck out of the chute. Once again, if the rider isn't successful in marking his horse out, then he will be disqualified.

A saddle ready to be used in the Saddle Bronc ride 

The rider holds onto a braided buck rein which is attached to the horse's halter. Like in other rough stock events he can only hold on with one hand, as touching anything with his free arm will get him disqualified. He holds on to this rein while trying to keep himself squarely and securely in the saddle. 

As the horse bucks the rider brings his legs from the horse's shoulders, where he made his mark out, to the back of the saddle. While doing this he attempts to keep his toes turned outwards in order for his spurs to maintain contact with the horse throughout the spurring motion. Like in the bareback event, the rider is judged not only on his actual ride but also on the quality of his spurring technique, balance, timing & control. He is required to the ride the animal for a full 8 seconds. 
How a rider can be disqualified: if he is bucked off before the required 8 seconds, if he touches the animal or himself with his free arm, if he misses his mark out, or if one or both of his feet come out of the stirrups during the ride