How do I wipe my MB Air's drive and start fresh? I want to return my Air to the original factory settings, to the way it was before I added all kinds of  junk to the solid state drive.

I'm running Snow Leopard. So after I wipe it clean, I plan to go to the App Store and buy Lion.
If you bought a pre-Lion Macbook Air, it should have shipped with a system restore USB drive. This is exactly the scenario for which it exists: restoring your system to factory condition. Back up all your data, so you can keep what you want. Then, plug in the restore drive, and hold down the option key (⌥) when you boot. Select the restore drive, and follow the instructions to install a clean install of Snow Leopard.