I wasn't questioning the replacement of the thermostat. But if you didn't notice any leaking
before the thermostat replacement, but there has been leaking almost continually
after the replacement, this indicates there is still something wrong with the thermostat installation because it's highly unlikely the water pump spontaneously died at the same time. I think you need to take it back to them and tell them it's still leaking.
The water pump is pretty simple. You can see it toward the front of the engine with the fan and fan clutch attached to it. Five bolts hold it to the block. Do you see any drips from it? Do you notice wobble in your fan when it's running? When you remove the belt, is there excessive play in the shaft of the water pump? If not, then it probably isn't your water pump. Our water pumps are notorious for wobbling and grinding when they begin failing and if not replaced will then start to leak fluid. You might need to remove the plastic oil pan shield to see where the leak is coming from (four 13mm bolts on mine).
Also, you waited until it was cool to check for leaks? I would start it and either prop up the hood, remove the driver's front wheel (you can see the thermostat through the wheel well), or slide under while it idles to watch for the leak (only do this when you are absolutely sure you can do so safely). An easier way to do this is to cut strips of white cloth and tie them at different places. For instance, but three of four at different points on the thermostat to radiator hose and one at the base of the thermostat. Then whichever ones are orange will indicate where it's leaking. Don't try this around the water pump. It'll be a tangled mess. But if you are seeing large puddles then it's a good sized leak and shouldn't be hard to find.
I was worried one time when I drove away from my parking spot (outdoors). I saw an orange puddle and thought it might be Dexcool but I couldn't find any leaks. Then I thought back and remembered I had used the windshield wipers to clean off the bug splatters. I use the orange RainX fluid... It was one of those days.