First decide if you want to do traditional or digital animation, or combine the two.
Animating something involves a lot of time and work. You can draw each picture individually, using a lightbox or something more technical, or draw different body parts straight on the computer, and animate them that way.
Getting the software called Adobe Flash (use to be Macromedia) is a good start... that's a program you can use to animate things. There are tutorials on the Internet on how to use it, but it will take some getting use to.
When beginning, try a technique called rotoscoping, some people call it 'cheating', but it's a fast and easy way to animate on programs like Flash (rotoscoping is tracing over an animation to get the same movement you want).
Two books I found really helpful with hand drawn animation were The Animator's Survival Kit by Richard Williams and Animals In Motion by Eadweard Muybridge (there is also a people version).
Here is a short animation I made for school a while ago: http://www.deviantart.com/deviation/22581247
It is not the best, but note it was my first try doing something like that, and decent for a first time I think.
I combined traditional and digital, there are better techniques out there, I am sure, note that I've never had schooling so pretty much just guessed what to do:
* Voices were recorded before animating the talking scenes.
* Every picture was drawn with the aid of a lightbox, inked, scanned, and then coloured using Adobe Photoshop.
* Backgrounds were drawn using Photoshop.
* Both the pictures and backgrounds were thrown together onto Flash
* Converted every frame to a .jpg file, then all the pictures were put onto Windows Movie Maker (nowdays I would use Adobe Premiere)
* Music was made in ACID Pro
* Text, voices, sound effects (sounddogs.com) and music was added on Movie Maker
As you can see this technique caused a white line halo over all the characters, this can be avoided by drawing straight on Flash.