First, you're going to want to stop by here and choose your animation program. For 2D most people here use Flash and for 3D the choice is yours really, but I recommend Maya.
Second, there is a list of flash tutorials here on Newgrounds you can check out. (along with other links to the left for sprites and other animation tutorials).
The best way to learn, in my opinion, is to practice. The more you practice the better you will get. Also, watch other animations and figure out how artists animate their works. That usually works for me. You can even reach out to them through PM and ask for tips. Most people here are nice and will respond relatively quick.