If you wanna get around in Palermo or Sicily you have many possibilities... the train or buses to go from a city/countrytown to another one... the airplane if you are going to palermo or catania which are the main cities in Sicily....
The train is definately the best! As it cross the straits be awake to see the train being split into shorter sections to move into a large ferry. As the ferry cross the straits, be sure to get off the train and climb to the top of the ferry for a great view! At night, its quite dark but the breeze is worth the flights of stairs up the ferry deck
Walk or take the bus.
Drive to get to nearby town. The train is great too for inter-town travel!
Palermo is connected by trains to all the major destinations in Sicily, such as Taormina, Catania and Siracusa.
For some destinations it is necessary to change trains.
From Rome there are some direct trains for Palermo via Naples.
the trip lasts 11 to 13 hours.
For times please consult the Trenitalia site or call the green number 89 20 21.
Probably the best way to get to Palermo from the airport is by moter coach (bus). They leave about every 45 minutes during business hours and the cost is about $8-$10 US equiv. (also see my general comment at home page for Frank_Petro). Out of and back into Palermo, I would strogly suggest taking the train. Much scenery along the way, and you can enjoy with out having to drive. Taxi's are much more expensive.
The Palermo Central Station, built in 1885, is one of Italy’s oldest operating stations. The architectural style is typical of the end of the 19th century.
Trains depart from this station to several places in Sicily.
You can get to Palermo by airplane, landing in Punta Raisi airport. flights from quite all Italian airports and some major foreign ones (London, Bruxelles, Paris). Then take the train to Palermo Central Station or the bus to Piazza Politeama.
If you want to visit only the city (and not the surroundings) don't rent a car that will only be a problem for you in the chaotic traffic of the center. You can also reach the city by way of sea from Naples, Genoa, Livorno and Cagliari, in Sardinia.
Moving across the city you can use the orange buses that cover quite all the area, taking you as far as Mondello, the wonderful beach of Palermo. They're trying to give the city an underground, but the service is very poor by now, so prefer the surface. Taxis are rather cheap, but the traffic is often jammed, so consider walking as a good choice. If you want to visit the outskirts of Palermo and the surrounding towns, rent a car in one of the many agencies or you won't be able to reach your lodging after some nightlife! Best choice is a scooter. Park on the sidewalks if you don't obstruct the passage, policemen will tolerate it.
I recently visited Palermo again (Jan 02) and was pleased to discover that since my last visit they had installed a train link from the airport to PMO centre, this is good news indeed for the tourist. Fair enough it only runs once an hour but at the same time its better than what there was before, which as far as I understand it was zero...