Not to be confused with circumcision. Castration is the removal of the testicles, used to neuter potential threats to society, and also done as a fetishistic thing by people who don't care about procreation. Also one of the results of sexual reassignment surgery.
There are many methods by which this is done. Most people would think of either the Burdizzo clamp or a specialized surgery. Doing it via surgery is much more risky, as the crotch is full of wonderful, highly-infectious bacteria
and fungus, and so the Burdizzo is probably the preferred method. Within the circles which castration tools
are much more acceptable (unlike on people who aren't animals and therefore are above tools designed for
farm use), the elastrator is probably used quite often as well, since there's less of an instantaneous risk of
poor migrant worker being fatally kicked in the gut while trying to crush the cords properly, and it's not
very likely that a bull would be able to remove the band, regardless of how much pain he is in (as comical
a thought that is). For human animals, however, it's probably risky surgery which is most common, then the
Burdizzo clamp, then the elastrator. I don't think there's a lot of statistics out there to back this up though.
The surgical term for castration is orchiectomy.