I know I'm a simpleton, but educate me fellas.

Say the guy at the gas station, or the waiter at the restuarant writes down my credit card number. Then what do they do with it? They can't go to an ATM or gas pump because they don't have the card. If they order anything online, they have to ship it to an address right? So how do they effectively use it? I'm sure its simple, I guess I'm to honest to think of a way of cheating the system.