I don't really know much about the animation process (this is the first 2D animation I've ever done on a computer), but it turned out ok, so I figured I'd just write down the process I did, with some thoughts about what worked and what didn't work, and some tips for the beginning animator. My style doesn't incorporate a ton of squash and stretch or cartoony looking characters, so keep that in mind...
1) Sketch out the animation in stick-figure form.