Hobby servos are the easiest way to get going with motor control. They have a 3-pin 0.1" female header connection with +5V, ground and signal inputs. The motor shield simply brings out the PWM output lines from Arduino pins 9 and 10 to two 3-pin headers so that its easy to plug in and go. They can take a lot of power so a 9V battery wont last more than a few minutes!
The nice thing about using the onboard PWM is that its very precise and goes about its business in the background. You can use the built in Servo library
Power for the Servos comes from the Arduino's on-board 5V regulator, powered directly from the USB or DC power jack on the Arduino. If you need an external supply, cut the 5v trace on the bottom of the board and connect a 5V or 6V DC supply directly to the Opt Servo power input. Using an external supply is for advanced users as you can accidentally destroy the servos by connecting a power supply incorrectly!