I have an original shower stall leaking in the basement. The leak seems to happen after the showers for the day are complete. I have rusting around the round shower base and stalactites forming from the leaky areas. My question is how do I determine if the leak is coming from the shower pan or somewhere else?

Lots of little test you can do to pin it down. 1. pour in a bucket of water drawn from another faucet. This will tell if it's the drain. 2. Remove the shower handle an escutcheon plate. Look inside with a flashlight to see if the valve leaks or the pipe up to the shower head leaks. You will need to run the shower to do this so take appropriate measures. 3. Use a garden hose to direct water along the caulk line between the wall and pan transition, this will check for a bad caulk job.

This is actually a shower stall, not a tub shower. I have added some pictures to show what I have.

My directions were for either a shower or a tub/shower, the approach is the same. Have you tried any of the tests yet, what did you see?

OK I have tried Test 1, To pour a bucket of water from another faucet down the drain. I have poured 1 gallon down the drain. I am not seeing anything aside from what has been dripping all day. 1-2 drops per 5 minutes or so. Will wait hour or so before I try step 2.

Ok I have the escutcheon plate off and this is what I am looking at. What do I undo next to see if it is leaking here? I can't see past the valve. Also I am seeing green corrosion around the cold water pipe in the basement. I have added both pictures.

Where does that copper p[ipe go in pic #2? It clearly looks suspect.

From the looks of you floor underneath the shower where the drain is, it looks like you have had some leakage problems for awhile. Also the pic of your faucet clearly shows a water level right up to the bottom of the tile. This means that your faucet cover plate is leaking at the top or sides, and holding water at the bottom until it fills up and runs down inside your wall. With a tile shower this old, I would say you either need to regrout the whole shower or serioulsly look at replacement with a fiberglass or acrylic unit. You can also have another custum tile showe built, but it will get very costly, you most likely would need a whole new backing system(cement board). Either way, its looks like its time for a remodel.
That said, one easy thing to try(if you don't notice any crack in your grout) is to silicone around your drain. Make sure the surface is completely dry when you do this. Please let me know what you find.