During the summer season (April-October) Sicily's international airports are connected by charter flights (non stop) to all major cities in Europe. All year round there are scheduled flights connecting Sicily to the rest of the world. Scheduled (particularly long haul) flights often stop over in Rome or Milan or another major European airport, depending on the airline.
The shortest way to Sicily is of course by airplane. The best connections are to the international airports in Trapani or Palermo.