"How does one actually go about shaving ones balls?"
You have to grab the scrotum, stretch the skin out, and shave the section of taut skin. Grab, stretch, and shave until you've shaved the whole area. I strongly suggest using a razor with at least triple blades. My preference is the Gillette Sensor3 because I hate the pivot geometry of the Mach3, but the Mach3 would probably work just fine. My habit is to do all shaving in the shower, but some guys dry shave their balls because the scrotum skin swells up with water, making it a less close shave once the scrotal skin dries out.