We highly recommend Rick's tip to take the "shared taxi". We found the shared taxi easy to find (follow Rick's directions) and relatively fast. Once the shared taxi fills-up (it's used by locals), we were taken to our hotel. DON'T EVEN THINIK ABOUT DRIVING A CAR IN PALERMO! Not only is it extremely congested, there is a "code of conduct" for navigating the city that you will never understand. I had to close my eyes multiple times, especially when the driver took a left hand turn! Additionally, I didn't see a parking place in Palermo the entire 3 days we were there.
Be sure to get the shared taxi driver's card when you arrive at your hotel. This way you can ask your hotel to call the driver and arrange a trip back to the airport on your departure. We rented a car at the airport to visit the rest of the island, and getting out of the airport and onto the motorway south is quick and easy.