In countries where you drive on the right side of the road (the US, and most European countries), you should signal with the left arm. That means:
- Turning right: signal with a 90 degree bent left arm out to the side,
- Turning left: signal with a straight arm out to the side, straight
The reason to use the left arm is that your left brake is the front wheel. If you have to brake in an emergency situation, it's usually better to heavily use the rear brake. If you only use the front brake, there's more of a danger of going over your bars.
In countries such as the UK, where you drive on the left hand side of the road, brakes are reversed. So signal with the right arm.
Generally, pointing clears up some ambiguity compared to a bent arm, but is less safe for the cyclist when turning right (or left in the UK, etc.).