The nearest airport is Catania airport, Catania Fontanarossa 40 km south. Take the Interbus from the airport towards Taormina. Get off at Recanati for south & central parts of town, and at Taormina-Giardini railway station for the north end. Buses run roughly hourly 07:00-20:00, taking 80 min, fare €8.20 (€7.50 if bought online). Use this same bus line from downtown Catania.
Taormina-Giardini railway station is at the north-east end of the town's seafront. There are trains roughly hourly from Messina to the north and Catania to the south, both taking just under an hour.
The Catania - Messina motorway A18 passes town, exit at "Giardini-Naxos" onto the main street SS 114.