Cement clinker is usually ground using a ball mill. This is essentially a large rotating drum containing grinding media - normally steel balls. As the drum rotates, the motion of the balls crushes the clinker. The drum rotates approximately once every couple of seconds.
The drum is generally divided into two or three chambers, with different size grinding media. As the clinker particles are ground down, smaller media are more efficient at reducing the particle size still further.
Grinding systems are either 'open circuit' or 'closed circuit.' In an open circuit system, the feed rate of incoming clinker is adjusted to achieve the desired fineness of the product. In a closed circuit system, coarse particles are separated from the finer product and returned for further grinding.
Gypsum is interground with the clinker in order to control the setting properties of the cement. Clinker grinding uses a lot of energy and the cement becomes hot - this can result in the gypsum becoming dehydrated, with potentially undesirable results - see the link at the bottom of this page for more information.