There is a good basic, animation program called Pencil. It is completely free, unless you want to make a donation. It's pretty good for a free thing!
Pivot Stickfigure Animator.... Its good....
You can do basic animation with Grisoft's GIMP, which is free.
stiks is a great program for that
Pivot Stickfigure Animator
There are many ways you can go about finding a good animation program. Finding a good program would depend on the budget your trying to spend, the animation that is going to be created, and the personal needs to be choose from.
AH! I found one! Called pencil! Awesome program!
You should not buy a animation program if you do not need too. You can find perfectly good animation software right online, such as blender.org. Blender is a free 3d animation prgram which can offer reasonably high graphics and can make movies, games, and a bunch of other things to. try googling blender.org
If you mean the program/software which is featured in the animation, its called Adobe Flash and you have to buy it or you can download a free trial see the related link below
You can learn how to use a free 3D animation program like Blender. A simple intro with just text and a background should be fairly easy to create.
The program used to create Family Guy and American Dad animation is called Toon Boom Studio. Alternatives to this program include Adobe Flash Professional, CreaToon, Plastic Animation Paper, and Ella, among others.