The Lyman #47 had an article with good illustrations depicting this, and I'm sorry it disappeared. If you are interested in the technical nitty-gritty, the
SAAMI Centerfire Rifle Standard has a description starting on page 160 (172, as Acrobat counts pages), but it will be beyond people unfamiliar with basic statistics and QC practices.
Basically, a SAAMI standard test barrel for a particular chambering is mounted in a universal receiver that accepts all SAAMI test barrels and serves as the ballistic technicians switch-barrel gun. The test barrels are different for copper crusher and for conformal piezoelectric transducer testing, and the Europeans have their own standard employing a channel type piezoelectric transducer that is yet another configuration.
The copper crusher barrel has a hole in the chamber that is specified as to location and diameter in the SAAMI specification I linked to. A small piston is placed in that hole. The old system required drilling a hole in the case to match that location, but that was a bother and later made optional. A kind of saddle clamp anchors an anvil over the piston location in the barrel. A calibrated copper slug is placed between the anvil and the piston. When the gun is fired, pressure in the chamber drives the piston to crush the copper slug against the anvil. The slug is then removed and a micrometer is used to measure how much it was crushed. The amount of crush is then looked up on a tarage table—a calibration table provided by the slug maker—and the pressure is read off that table for the amount of crush that was measured.
This method used to be used to determine psi. However, when piezoelectric and strain gauge testing was used for comparison in the 60's, it was discovered the copper crusher system was non-linear and as the pressure got higher its readings were too low. However, it was still possible to use the instrument to compare a reference load to a new load being developed using the old apparatus, so rather than abandon it, SAAMI gave the old instrument its own unit called the CUP for Copper Unit of Pressure so it would not be confused with actual psi (pounds per square inch). Nonetheless, you have to be careful reading pressure data to be sure you are not seeing older data for which the copper crusher result was still reported in psi instead of in CUP. All the older military manuals, for example, still report copper crusher results as psi when they are actually CUP. Any military technical manual not published after about 2000 may have that confusing data. Older publications like Hatcher's Notebook (the last edition was 1961) still refer to copper crusher measurements as psi.
One other problem with the copper crusher, besides its non-linearity, is that it is less consistent than the other methods by about a factor of two, so even for comparison, it is a less desirable method of measuring. The military produced an improved M11 copper crusher tester in the 1970's or 80's that was apparently more consistent, but not adopted commercially, AFAIK.
The cause of the non-linearity is that the copper slug calibration is static in which the psi for the tarage table are measured crush produced by weights bearing on a piston like the ones in the crusher barrels. That is a static test that deforms the metal a bit more than happens in an actual test at the higher pressures. Those higher pressures have very brief peaks that occur so quickly the inertia of the piston and slug absorb some of the force before deformation progresses fully. The system could be made much better if dynamic calibration were done, but the lower consistency as compared to other methods would still be present. It is due, in part, to the fact no two ballistic technicians seem to have identical touch with the micrometers used to make the measurement. Maybe that could be addressed with a laser micrometer, but nobody would bother now. Everyone likes the complete pressure traces produced by the transducer and strain gauge instruments, and there is no way for the crusher to do that or to measure more than the peak value.