Like any other sport, there are a lot more rules in curling than it would first appear. Beyond the official rules, and perhaps more importantly, curling is a sport that is based largely on honesty, fair play, and good sportsmanship. The ethical code is known as the "Spirit of Curling" and reads:
Curling is a game of skill and traditions. A shot well executed is a delight to see and so, too, it is a fine thing to observe the time-honored tradition of curling being applied in the true spirit of the game. Curlers play to win but never to humble their opponents. A true curler would prefer to lose rather than win unfairly.
A good curler never attempts to distract an opponent or otherwise prevent him/her from playing his/her best.
No curler ever deliberately breaks a rule of the game or any of its traditions. But, if he/she should do so inadvertently and be aware of it, he/she is the first to divulge the breach.
While the main object of curling is to determine the relative skills of the players, the spirit of the game demands good sportsmanship, kindly feeling, and honorable conduct. This spirit should influence both the interpretation and application of the rules of the game, and also the conduct of all participants on and off the ice.
The actual rules of the game are many, and you can read them on the Curling Basics website. In some cases the rules have been animated for further clarification. Rules for both the World Curling Federation and the Canadian Curling Federation are listed there. Though they are not the same in all aspects, they are close enough to get you started and give you an idea of what you can and can't do.
You can also view the United States Curling Association Rules.