The best airport is Italy Naples International airport (NAP), which should be reachable through direct flights from many European hubs.
From Naples International airport there is a direct shuttle to Sorrento, operated by Curreri, it takes about 70-90 minutes to get to Sorrento, depending on the traffic jam. Alternatively, there is a continuous shuttle called Alibus (2-3 rides per hour) taking to Naples’ railway station in 20 minutes, from which Circumvesuviana’s trains go to Sorrento in about 1 hour.
People flying to Rome can either go to Naples’ railway station through Flixbus or Fiumicino express buses, or catch the Leonardo’s train to Rome’s railway station, from where high-speed trains connect to Naples in about 70 minutes.
Curreri and Alibus tickets can be bought on board, as well as Flixbus and Fiumicino Express.
Circumvesuviana railway has its own ticket offices at the station, or they can be bought through the app Unicocampania. The timetables can be consulted online on the company running the railway, that is, EAV (Ente autonomo volturno).
Both Leonardo and High speed train tickets can be purchased either at the stations or from the website of Trenitalia.