When we got our 500 I had a tough time with it also. I was used to double-clutching but with a sports car. In the 500 you have to be patient. You can't just blip the gas like in other cars. If you want to go from 3rd to 2nd for example you have to push the clutch, shift to neutral, release the clutch and mash the throttle. Wait for the engine speed to come up (the trick is to know how much-for a shift at the bottom of second gear use a lower engine speed but to go towards the top of second gear you really need some engine speed)- now get off the gas a little, push the clutch and change down to second.
To upshift you have to pause a half second in neutral and wait for the shaft to naturally loose speed so it will mesh. to speed this up you can double clutch the upshift but you do not need to add the gas.
Now the fun part. Downshift while braking down a hill. You need three feet but you only have 2. This is where you have to mash the gas with the side of your foot while working the brake with your toe.
With practice you will get perfectly quiet and smooth shifts.
Very satisfying and adds to the fun of the car.
Ciao,
dave