Replacing a balance staff entails using a lathe to cut away enough of the old staff (if it is a swaged on staff), to allow the damaged staff to be pressed out of the balance. The vital thing is to not distort or damage the balance. Then a replacement staff can be installed and swaged into place. Then the whole balance needs to be checked and perhaps poised. Some watches do not allow replacement parts to be just swapped in. A replacement staff may be too short or too long, or need some adjusting to fit the specific watch. A lathe will almost certainly be needed in such cases.
Some more modern watches have interchangeable parts. I have been told that you can take apart several Hamilton 992B watches and then put them all together without concern about which parts came from which watch, but I don't think I will actually try it.
Some Waltham and Hamilton watches have friction fit balance staffs. This makes repair a lot easier, but care must be taken to press the staff out of the hub (which is typically a different blue color). The hub stays with the balance. Sometimes people make the mistake of pressing the staff and hub out of the balance as they would for a normal staff replacement, and this leads to undue troubles.
Here are my notes on
The following links discuss replacing the staff in a Hamilton 992B:
Tom's notes / [email protected]