Step 1: Go to your favorite hardware store, and buy a wide angle door viewer.
You should be able to find one of these at any hardware store. I got mine at Home Depot for about $11. The key attributes that you're looking for is the largest possible "eye hole". There are a bunch of these door viewers that have very small openings, and they won't produce a very good image. Get the one I'm showing here, and it will work great. The opening is just about the size of the lens on my old Canon S230.
Step 2: Take some pictures!
Remove the threaded backing from the Door Viewer, hold it directly on the lens of the camera, zoom all the way in, and start taking some pictures! Some cameras may have a bit of trouble focusing, so if your camera has a center-weighted mode, turn that on to force it to meter and focus on the center of the image. It also seems like using the "macro" mode helps focusing as well, since you usually need to get really close for the best wide angle effect.
Step 3: Edit photos in The Gimp or Photoshop.
The photos don't necessarily need to be edited, but doing so will create a nice effect. All you need to do is use the circular select tool to crop out the circular image, and black out the rest. Using "guides" will help with the positioning of the circular selection.