So how do you get started? Well, first...
Learn the Basics.
Understand the basic principles, the terminology, the techniques - what frame rate is, the importance of key frames, how traditional animation works, what in-betweening is, the various methods of animation, why aspect ratios make a difference. Do your research, learn the lingo, and build your foundation, until you understand character design, understand how a sequence of drawings can become a moving picture, and understand that it’s a time-consuming process that requires a great deal of patience. Try sketching a few walk cycles. Make a flip book. Draw a few character sheets. Learn about principles like squash and stretch. You can find numerous lessons online, but there are also hundreds of books that can be invaluable when it comes to learning the principles of animation. Heck, just watch animations as much as you can. Take what you’ve learned from studying and just observe, and see how it’s applied. See if you can figure out how various things were done.
Decide What Path You Want to Take.
Do you want to be a traditional animator or a digital animator? Are you interested in cel animation or stop-motion, 2D or 3D animation? Some people focus on only one discipline, while others go the "jack of all trades" route. Knowing what you want to specialize in will help you take the next path, which is...
Select Your Tools.
You may be working with blue-line pencils, paper, and light tables - or going wholly software-based with a desktop computer and Flash, Maya, or any number of other programs. Just picking the software you want to work with can be grueling in and of itself. Different animation paths require different tools; you may have an entire studio scattered with freshly-painted cels, or your entire workspace may be confined to your laptop (or multiple computers, especially if you’re working with resource-heavy 3D renders). You may even work with hybrid techniques, pairing traditional techniques with digital effects. My personal workflow generally involves hand-drawing line art on paper - then rather than copying to cels, instead I scan them into my laptop, clean them up in Photoshop, edit out the empty background, before using a layered file to fill in the color and shading. After that it’s a matter of importing into Flash to sequence and layer over the background. Others prefer to use tools like graphics tablets to draw on-screen, without ever touching pencil and paper.
No, seriously. Practice. Practice a lot. Practice until you’re getting carpal tunnel syndrome from cramping your fingers around a pencil or clutching a mouse, and then keep practicing. And when you’re not practicing, observe. Study life around you, study the way objects interact with each other, study the way things move, and learn how to translate that into your animation medium. Experiment. Find the methods, tools, and medium that work best for you, and then practice even more.
Animators never stop learning, ever. There’s always a new way to do things, or simply something we haven’t tried before - and animation isn’t easy. Not by a long shot. Even with tools such as auto-tweening in Flash or bone systems in Maya and 3D Studio Max, your first animation will suck. Period. That’s just the way it goes. Your next one probably will, too. And your third.
But with practice you’ll keep getting better and better, and keep expanding until you’re producing the visions that made you want to become an animator in the first place.