The practice of using hand signals in traffic is largely obsolete. Modern motor vehicles use electrically-controlled lights to signal a turn or stop. These signals, originally intended for general use and still taught in drivers' education courses, are now most often used by cyclists, and occasionally by motorists whose vehicles aren't working properly. I'm assuming here that traffic is flowing on the right side of the road and the driver's seat is in the left of the vehicle, as is the case in North America.
Right Turn
Extend your left arm out the driver's-side window and bend upward ninety degrees at the elbow. This signal (as well as the other two) should be given with an open hand; a similar gesture with a closed fist is often used as a greeting by interstate truckers.
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Left Turn
Extend your left arm straight out the driver's-side window.
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Stop
Extend your left arm out the driver's-side window and bend downward ninety degrees at the elbow.
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Also, qousqous mentioned that a cyclist can signal a right turn by fully extending their right hand. | 
