You will need:
= one or more dry erase boards
(more than one is nice because you can do multiple scenes at the same time without erasing the same board over and over)
= a usb camera
I use a logitech quickcam chat, it's cheap and does the job. It also comes with a weird bendy mount which allows me to mount it on a tripod that I have.
= a computer
any old computer will work as long as it can run the software (see below)
= some free software
I use 'MonkeyJam' to make the initial animations, it's free and it's great, does everything you need to make nice animations.http://www.giantscreamingrobotmonkeys.com/monkeyjam/download.html
I use 'Video Edit Magic' to do the post animation editing (adding music, sound effects, naration, etc). It's a very cheap, simple, and effective program.