Already mentioned, pour 1 gallon of bleach into a 5 gallon bucket add water and then pour diluted bleach into the well. There is a formula as to how many gallons of bleach per size/depth of well should be used (do a search on-line sure ones is out there as a rule of thumb.)
Run hose out and back into well until bleach water is coming out of the hose per smell. Use the hose to wash the casing down real good so the bleach water comes into contact with the casing as best you can. shut down the hose and run the fixtures in house (all of them including flushing) to get bleach water into them.
It is best done late at night or early in AM and leave the bleach water in the pipes 24+hrs, DON'T DO LAUNDRY

. It will not harm the PIPES/FIXTURES, it can cause some rubber deterioration in rubber seals in toilets but for small amount of time it is going to be there overnight or all day it is fine. The reason I suggest 24 hours of bleach in well/lines/fixtures to be sure it kills it off any and all bacteria.
On my well it calls for 1 gallon of bleach from when I looked it up long time ago, I don't use it all that often in winter (cabin) so spring it gets 2 gallons and sets for a few days with it in everything.
FYI the "Pool Shock" stuff should normally NOT be used some of it is bleach based others are not and can be poisonous (more so than the bleach.) If you use the bleach based pool shock it is not as effective as it is timed lower release or drops to bottom of well and does not mix well to give a SHOCK to kill everything at once.
After the 24+ hours as mentioned run well till bleach is gone out away from septic thru hose in driveway.
Mark