Sorry Kelburn I should have answered your question when you first posted it.
Animators use a variety of programmes to create animations.
I don't know what your level of ability is in this field but I would start with something like Adobe Flash.
http://www.adobe.com/products/flash/Cartoons like Family Guy, The Simpsons, Futurama etc use a programme called "ToonBoom".
Which bare in mind is a big expensive commercial programme and is a steep learning curve.
In my opinion I would use flash if I was you, its pretty easy to learn (if you don't know it already).
I think you can pick up a student version for pretty cheap to.
Che