Just a month ago, our geek wish of getting a 3D printer was granted: a Makerbot Replicator 2X arrived at our office. Since then we've been busy learning by trial and error about the possibilities and limitations of 3D printing. You can read my review of the Printrbot Simple Kit.
So far, in short, I can describe 3D printing as: Building an object, by depositing layers, and creating every layer by drawing it with melted plastic. The key to understanding 3D printing, and thus learning how to do it better, is to think about the objects as a stack of layers. Then, consider how the layers will look like as they are being stacked.