By air:

Sicily is served by 'regular' and low-cost airlines in its three airports located in Palermo, Catania and Trapani, as well as airports on the satellite islands of  Pantelleria and Lampedusa.

Check this site for current and accurate information for (direct) flights to Sicily from mainland Italy, as well as major European hubs.

http://www.thinksicily.com/travel-to-...

By ship:

There are ferry connections to Palermo from Genoa, Cagliari, Civitavecchia, Livorno, Naples, Salerno, and Tunis; to Catania from Naples and Malta; to Trapani from Cagliari.  A good search engine to find all connections, schedules, fares, etc., is www.traghetti.com.

Additionally, there are very frequent connections between Messina and Villa San Giovanni and Reggio di Calabria in Calabria, on the tip of the Italian peninsula.

By rail:

There are direct train connections to Palermo and Catania from the Italian mainland. Trains are actually loaded onto dedicated ferry boats for the crossing. Schedules on http://www.trenitalia.com/en/index.html

By bus:

Because trains are slow and tedious in Sicily, Sicilians prefer travel by bus - Buses are faster, convenient, clean, and reliable, have air-conditioning, and buses reach areas not served by trains.

There are bus connections from Palermo and Catania to Rome and other cities on the Italian mainland.

Driving:

For many years there has been talk of building a bridge connecting mainland Italy to the island, but until recent years it has been a very unpopular idea. Recently, however, the current mode of thought has been that it would be economically beneficial to link up with the mainland. There were heated debates on this topic during the elections for a new Prime Minister. Even if the decision was made to build a bridge, it would take years for completion. The bridge would have to be several miles in length.

Until such time as the bridge is completed, you can certainly drive to Sicily, but will have to use a ferry boat from Villa San Giovanni to Messina (or use one of the ships coming in from other Italian ports -- see above).