To reach this wonderful piece of paradise, the closest airports are Catania, Palermo, and Naples.
Catania Fontanarossa (CTA) is the closest and suggested airport. From Catania, you will need to take a bus (approx 1,5hours), and finally, a hydrofoil /Aliscafo (approx 1,5 hours). To ensure you catch the last departing boat to Salina, the arrival time of your flight should not be later than 3 pm. On your day of departure, please make sure to book your flight after 11 am to ensure enough time to get off the island and reach the airport. If you manage to depart in the afternoon, you will have a more comfortable commute.
Below all the links for transportation from the closest airports: