To control a motor using the Arduino Motor Shield, first plug the motor's positive (red) wire into Channel A's + terminal on the motor shield, and the motor's ground (black) wire into Channel A's - terminal on the shield.
An external power supply is not always necessary, but it drastically improves the motor's performance. It is recommended that you always use one.
To connect your external power supply, connect the positive (red) wire from the power supply to the "Vin" terminal, and the ground (black) wire to the "GND" terminal.
Finally, upload the code to control the Motor Shield to the Arduino.
Here is the code for controlling one motor: