An Arduino can control a motor with a motor shield.
For example if you want to spin your camera around with 1000 rpm.
Or do you want a motor with a gear ?
You will perhaps also need sensors to detect the rotation and tilting angle.
An Arduino can control a servo motor without motor shield.
Just connect a pin of the Arduino to the signal wire of the servo.
You need a good seperate power supply for the servos.
The Servo library is easy to use.http://arduino.cc/en/Reference/Servo
Controlling the speed of the servo is not very easy.
How do you track the point the camera the looking at ?
What kind of motors do you want to use ?