How were Eunuchs castrated?

The magnitude of the question runs from at least the Assyrians (probably earlier) until now, and covers many major civilizations. Add on to this, many societies had more than one way to skin a cat, some societies having more than one variety of eunuch on top of that, and a general taboo about the procedure leading to a muddled mess of 3rd party rumor-reports and outsider travelogues as our main basis of information on how to make a eunuch. This is also probably the most boring aspect of eunuchs to me to be honest! It's like you study the history of steamships and everyone asks what iron they used.

There are two basic types of eunuchs in history, “clean-cut” (no penis or testicles) or just a removal of the testes. A simple removal of the testes is historically the most common sort. There’s a third type where the penis was removed but the testicles left, but it’s only referenced in a few places for Islamic eunuchs and seems to have been a very limited thing, and there’s really no reason to do it like this other than punishment.
For clean-cut eunuchs there was basically only one method, cutting it all off in one go which has been described for the Ottoman black eunuchs, and here’s the Chinese version from G. C. Stent who is probably our most reliable Western reporter:

When the operation is about to take place, the candidate or victim--as the case may be--is placed on a kang in a sitting--or rather, reclining position. One man supports him round the waist, while two others separate his legs and hold them down firmly, to prevent any movement on his part. [...] with one sweep of the knife he is made a eunuch.
The operation is performed in this manner:--white ligatures or bandages are bound tightly round the lower part of the belly and the upper parts of the thighs, to prevent too much hemorrhage. The parts about to be operated on are then bathed three times with hot pepper-water, the intended eunuch being in the reclining position as previously described. When the parts have been sufficiently bathed, the whole,--both testicles and penis--are cut off as closely as possible with a small curved knife, something in the shape of a sickle. The emasculation being effected, a pewter needle or spigot is carefully thrust into the main orifice at the root of the penis; the wound is then covered with paper saturated in cold water and is carefully bound up. After the wound is dressed the patient is made to walk about the room, supported by two of the "knifers," for two or three hours, when he is allowed to lie down.
The patient is not allowed to drink anything for three days, during which time he often suffers great agony, not only from thirst, but from intense pain, and from the impossibility of relieving nature during that period.
At the end of three days the bandage is taken off, the spigot is pulled out, and the sufferer obtains relief in the copious flow of urine which spurts out like a fountain. If this takes place satisfactorily, the patient is considered out of danger and congratulated on it; but if the unfortunate wretch cannot make water he is doomed to a death of agony, for the passages have become swollen and nothing can save him.

The exposed urethra would form a standard stoma. Scrotal tissue healed with some cicatrix formation but really nothing too dramatic. There are some historical drawings and photographs of this but I do not link to them in here as they were obtained non-consensually. Google “stoma” if you really need to know though, they all form the same looking thing really.
For removing the just the testes, you’ve got a few more options.

• Crushing the testes inside the scrotum with no cutting, most likely used for Assyrians (through some context clues I can go into), reportedly used for young boys and infants in the Byzantine empire, and also reportedly used for Italian castrati.
• Cutting the scrotum open and removing the testes. This is rather finicky but one method reportedly in use in Italy during the heyday of the castrati.
• A full removal of the scrotum with testes inside. I don’t suppose you do any livestock farming? This is the method in which the “castrator” tool was for, which are still used for livestock. It would often be heated to cauterize the wound right off, which prevented infection.

 Courtesy: "http://www.reddit.com/r/AskHistorians/comments/21btwr/how_were_eunuchs_castrated/"