This is the information I received from Dr. Larry White, DVM, who is a well-known local turtle expert. Dr. White himself keeps many pet turtles, and he also treats them in his practice. I am posting this here in the hope that the mods will make it a "sticky" so that when people come here, they can see this. Please note that these instructions are for MINOR, SURFACE-area shell breaks; any injury that intrudes into the body cavity or rips the turtle's skin is NOT MINOR and is cause for immediate verterinary attention.
I am NOT a veterinarian and I assume NO responsibility for your turtle's well-being. I am just passing this information along.
In the case of a minor shell break, look at the break.
1) Is it bleeding? Look carefully in bright light, because the blood is dark-colored and so is the shell. If bleeding, use a CLEAN towel to apply pressure until the bleeding stops.
2) One you stop the bleeding, you must do the following:
--i) Stow the turtle somewhere warm, dark, and dry. You can put it in a storage box with a clean towel for substrate.
--ii) Go to a pharmacy right away, AS SOON as you stop the bleeding. Get a soft or extra-soft toothbrush, and a bottle of Hibiclens or Betadine. These are cleansers made for wound care. DO NOT just buy any antibacterial soap.
--iii) Using the toothbrush, Hibiclens/Betadine and warm water, scrub the wound thoroughly for several seconds or as the instructions on the bottle say. (Your turtle will not like this. If it gets snappy, let it bite a towel to keep its mouth occupied.)
--iiii) After cleansing, put the turtle back in its dry place for at least four hours. longer is better- you want the wound to dry and scab. (I like to do this before bed and leave the turtle in "dry dock" all night.)
--iiiii) Repeat the cleansing and dry dock nightly until the wound is healed. inspect the wound EVERY DAY. Importantly, SMELL the wound every day. If it ever starts to smell bad, take the turtle to the vet immediately: foul smell is a sign of infection.
THIS POST IS NOT A SUBSTITUTE FOR VETERINARY TREATMENT. IT IS ONLY "FIRST AID" AND SHOULD ONLY BE USED FOR MINOR SHELL WOUNDS.
3) Is the shell soft? Does it smell? Is it discolored? If the answer to any of these is "yes", then see a vet.
4) If the shell is not bleeding, and is not soft, discolored, or smelly, then you probably have nothing to worry about. Dr. White told me that sometimes a piece of shell will 'die' for no reason and snap off. It is not a danger to the turtle.