Palermo is connected to the rest of Italy and Europe thanks to its airports:
Palermo International Airport (PMO), about 32 km west of the city
Trapani Airport, for low cost flights, with bus transfers to Palermo city
The Port of Palermo is connected by ferry to major Italian ports including Genoa, Civitàvecchia, Naples, Valletta (Malta) and Cagliara (Sardinia).
You can reach Palermo by train, coming from Rome or Naples, via the train ferry across the Strait of Messina.