Last night, my second floor shower wouldn't turn off because the handle cartridge broke and water leaked from the shower handle opening to behind the shower walls and all the way down to the garage. The water was dripping through the ceiling of the garage. This morning everything looks dry, but I'm sure I need to have it checked for standing water damage. Who do I call, what kind of repair needs done, about how much?
diceless is right about drilling holes to let out any water. If you get all of the water out quickly, chances are you will only be left needing to patch the holes you drilled, which is pretty easy. If a lot of water comes out of any spots, you may want to cut a small square hole (like 3x3) to make sure all of the water comes out and to allow air to get in for drying out. Then you can get a patch kit from the hardware store to fix the hole.
Drywall is fairly resilient and can tolerate a moderate amount of water for a short period of time, especially if the ends did not get wet.
And if it dries out quickly enough you will not have any mold worries.
So get drilling those holes!
First, start with your home insurance. You pay for it, might as well use it for cases like this. Water damage can be costly or it could just be a let it dry and patch a couple of holes. You will not know until things get checked out.
If you think you might have standing water on the garage ceiling, drill a couple of small holes where you think it might be. If there is water, you will know it. It is best to get rid of it before it causes more damage.
And call a plumber to replace the cartridge (insurance will not cover this cost).