It seems quite easy; paper shredders work by putting a paper in it. The little teeth eat it up. When the paper is done being chomped, it stops. There you are!
But when you actually get into the logistics, you can start to get lost. How does the machine know when paper is in it? How does it know when the paper stops? Would it do the same thing to -- say -- my hair, if it had the chance?
Let's get the basics down first, and talk about the smaller shredders we're used to seeing around the office. Shredders usually either cut the paper into strips or confetti-like squares. The paper shredder itself usually consists of a receptacle or bin where the shredded bits of material land. The top of the bin is fitted with a lid where the paper is fed into a slot. Strip-cut shredders may use rotating knives to cut the paper, while cross-cut shredders may use two sets of teeth that rotate in opposite directions to get a much smaller, square particle [source: Dahle Shredder]. When paper (or another object) touches the cutting head, a sensor activates and the sharp teeth or knives rotate and pull the paper into their jaws until the paper lies pathetically in pieces in the bin. Keep in mind that there's another set of sensors on the bottom of the lid; when the machine rests on top of the bin, it activates those bottom sensors, which then turn on the sensors that rotate the teeth.
In other words, the machine head must be firmly in place for the device to work properly, which is a fail-safe against it turning into a land-based "Jaws" before being properly in place. Even more helpful, a lot of shredders have an emergency shutoff feature that allows you to turn off the power to the teeth quickly.
Big, industrial shredders work much the same way. But instead of feeding a paper (or stack of papers) in at a time, they'll generally have a large hopper that you can toss documents into. These machines are quite a bit bigger, so they can grab larger materials with the teeth that pull them through. A lot like the small paper shredder, just on a larger scale.
And the scale does get large. Think about all the reasons we need not just paper shredders, but material shredders: Ever wonder how our garbage gets packed tightly into neat bales to make room on cargo ships or landfills? They go through shredders first. Or what about breaking down plastics for recycling? Shred 'em first. Naturally, even wood chips for playgrounds need to be shredded.