Falcone–Borsellino Palermo Airport (Punta Raisi): Use the Prestia e Comandè airport bus for the most straightforward run into central Palermo: about 50–60 minutes to Palermo Centrale, roughly €6–7, usually every 30 minutes. The airport rail service from Punta Raisi to Palermo Centrale costs about €6.50 and takes just under an hour; it is the better choice if your accommodation is near a station on its route, not automatically if you are staying around Teatro Massimo or Via Roma. Skip an airport taxi unless a late arrival, heavy luggage or a group makes the premium worthwhile.
Palermo Centrale railway station: This is the useful arrival station: at Piazza Giulio Cesare, on the southern edge of the historic centre. Ballarò, Kalsa and Via Roma are walkable; for the Norman Palace/Palatine Chapel use bus 109 or take a taxi rather than dragging luggage uphill through the old town. Long-distance and overnight trains from mainland Italy arrive here, including services carried across the Strait of Messina by train ferry.
Port of Palermo: Ferries from Genoa, Civitavecchia, Naples, Cagliari, Valletta and Tunis arrive at the port, north of the core centre. It is a short taxi or roughly a 20–30-minute walk to the Teatro Massimo/Via Roma area; do not assume a seamless rail-style terminal transfer.