I just did it on my 3.7L Commander this weekend, its easy peazy....
Either the seal on the water pump shaft fails or the seal between the body and engine fails. If the seal on the shaft failed, then at least the bottom half of the pump body would be wet and the pulley would be slinging the leaked coolant everywhere (sounds like your case). If its just the seal between the pump body and engine, the body of the pump should be fairly dry and NOT slinging off the pulley, obviously the seal itself is a lot cheaper than the whole water pump. You can't replace the shaft seal on the water pump yourself, you just have to get a new one.
I've read a lot of water pumps, even new are NOT lasting very long at all, the industry is just pumping out bad crap. The only aftermarket water pumps people are NOT saying bad things about are AC Delco and Gates, perhaps Beck Arney.
So either get the OEM water pump or one of those. I got the NAPA new water pump, Tru-Flow? which is really Gates (Gates is clearly printed on the pump body) for $60. It comes with a gasket in the box.
I also got a new pressure cap, they do go bad and will cause overheating if they can't hold pressure.
Remove the accessory belt.
You'll have to unbolt the idler wheel on the tensioning arm closest to the water pump to get access to one of the water pump bolts behind it.
Put a pan under the front of the engine to catch the anti-freeze.
Pull the bolts and pull the water pump off.
Three of the bolts are longer than the rest, they pass through the timing chain cover and bolt into the engine block, they have residue of thread sealant on them. So get some Permatex Hi-Temp thread sealant and put it on the threads of the longer bolts.
Clean the gasket surface on the engine.
Insert the gasket into the water pump.
This gasket seems like one of the newer silicone shaped gaskets, designed to work without any sealant, in fact using RTV or other sealants with them usually causes a leak, just bolt it up dry or a little wet with the coolant.
Bolt up the water pump, tighten down in a criss-cross fashion.
Bolt on the idler wheel you took off the tension arm.
Reinstall the accessory belt.
Fill with Coolant
Don't forget to use the correct coolant, either Dealer Chrysler HOAT or Zerex G-05. NAPA sells G-05, mix it 50/50 with distilled water.
While you do the job, draining and flushing the cooling system if you need it soon, is smart, it will be half done while doing the job. Replacing the accessory belt is smart if you need it soon, since you have to take it off and put it back on anyway.