The most basic form of cheese grater is a flat piece of metal with plastic or wooden handles. This can be rested on top of a bowl or held by one handle while the cheese is pressed against the sharp side. Most flat graters have several sizes of holes to achieve differently sized shreds. Flat graters are usually the least expensive variety, and are usually about $3-$5 US Dollars (USD.)
A bell grater is shaped like an old-fashioned cowbell, with four sides each featuring a different type of grating hole. These somewhat pyramid-shaped metal graters are held against a perpendicular surface to use, gathering the grated cheese underneath the tool. These graters are common and inexpensive, generally costing no more than $10 USD.
A new variety of cheese grater is the rotary grater. These cheese graters allow you to place a wedge of cheese inside the tool and crank a knob or handle to achieve the shredding. Rotary graters are a bit more expensive than bell or flat shaped graters, normal between $15-$25 USD.