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The closest airport to Sorrento is Naples [NAP]. There are several ways to get to Sorrento from the airport.

Taxi

A taxi from the airport direct to the hotel costs approximately €130.

Train

There is a short journey to the station from the airport, via bus or taxi.

You can catch the train to Sorrento via the Napoli Centrale–Sorrento Circumvesuviana, and then from Sorrento station you can reach the hotel by taxi or shuttle bus.

https://www.trenitalia.com/en.html

Bus

The Curreri Bus Service runs an efficient service from the airport to Sorrento Station. Journey time is approximately 1.5 hours, but it is excellent value for money. You can pre-book tickets on the website and they have a handy video demonstrating where the bus picks up from the airport!

https://www.curreriviaggi.it/

From Sorrento to the hotel

You can pick up a taxi outside the railway station, or the hotel runs a free shuttle service from the town to the hotel. The pick-up point is close to the train station as detailed on the map below.

Details on the following page (scroll down to Shuttle Service):
https://www.vesuviosorrento.com/en/services