It's a lot simpler than it appears, haha. First, I find a screenshot that looks good--it has to be a shot where their entire body (or almost all of it) is clearly visible. I vector the image in Illustrator, then bring it into InDesign and texture it with stuff I have in my own library or from Lost and Taken, an amazing high-res texture website. I do the layout in InDesign (on an A3 canvas, actually, so I can turn them into posters later if I want) and then it's a quick trip to Photoshop for a resize and some final adjustments.
All in all it only takes a few hours per piece, depending on how complex I want to make it. Lately I've been challenging myself to vector it in as few pieces as possible. For instance, Aang only has six discrete shapes, excluding his tattoos.