To do their jobs, shredders have to do two things: to snatch the paper from the feeder and to move it through the machines, and to do the actual paper demolition.
The snatching/moving mechanism is composed of rollers of various sizes and materials. There is at the top of the paper flow a guide to keep the paper more or less in line as it goes through the machine; this is needed to stop perpetual jamming. The paper doesn't have to be far off the vertical before it starts jamming up at either side of the machine! Below this are the rollers. There may be just one at each side of the paper path, for low-performance units, or several at equal intervals across the width. The wider the paper path and the more sheets at a time that can be fed, the more rollers there will be. They keep the paper moving - although once it hits the blades the rollers are out of the process - at a steady rate keeping the mechanism fed and the feed slot clear.
The actual cutting mechanism varies depending on whether the machine does strip-cutting or cross-cutting.
Strip-cutting is done by a couple of methods. There may be a number of wheels that do the job: they are very sharp, of course, and are serrated, rather than just circular. They are also set up so that the serrations aren't in line, wheel to wheel, but are a little bit out of phase. This is in case the paper stops moving below the rollers: if there were no serrations, the wheels would exert no pulling action on the paper - the unit would just spin endlessly. But the serrations, as well as cutting, yank the paper along through the machine; and since they're out of phase there will always be at least one serration in contact with the paper at all times, thus keeping it moving.
Higher-duty strip-cutters employ a slightly different mechanism: instead of wheels they employ serrated blades, which are moved up and down by the motion of the frame to which they're attached. It will be appreciated that much more cutting power can be applied, both by varying the angle of the blades slightly and by increasing the horizontal (to and from the paper) movement of the frame.
Cross-cutting shredders employ a more sophisticated mechanism. Two sets of serrated blades, deployed at an angle to each other, are used sequentially to cut one way then the other, resulting in very thoroughly chewed-up bits of paper. Mechanical or electrical timing devices keep the blades going at the proper tempo and speed; these are attached to or controlled by the motor driving the rollers, to make sure that all the parts work together properly.
One step up from cross-cutting, but some way below high-security devices, are the micro-cutters. These are cross-cutting machines in function, but which produce much smaller pieces, typically 3 mmm x 9mm.
That covers the basic mechanisms. There are fancifications to do with sensors: paper jams, blade problems, output container full, and so forth. Some shredders have settings to vary the action of the blades depending on the exact workload, or the speed of the machine. Such things will be explored as appropriate in other articles.