Naples to Sorrento
The closest airport to Sorrento is Naples Capodichino (NAP)
You can easily reach Sorrento from Naples by car, train, ferry, or private transfer. Getting from Naples to Sorrento by driving can be more than a thrill (terrifying for some) since most of the road zigzags on the edge of a cliff! Even so, if you elect to rent a car, you will be rewarded with stunning vistas and scenery. Other than driving, there are several other options for transportation to Sorrento. 
I’ve found that the least expensive choice (train) takes the longest time. Furthermore, it could be the most crowded and inconvenient with luggage. I find that the moderately priced option (ferry) is an easy way to go. The fastest and most comfortable (private driver) is the most expensive. In my opinion, there are things worth splurging on, and things worth skimping. Safety, time, and convenience may be worth the splurge for you.
Naples Airport to Sorrento Options:
Sorrento by Car:
From the Capodichino Airport or the Naples Central Train Station start by following signs to Tangenziale-Autostrade. Then take the A3 Highway/Salerno-Reggio Calabria. Continue to Castellammare di Stabia exit. Then take the 145 state street and follow directions to the Penisola Sorrentina. Welcome to Sorrento!
Naples to Sorrento Train
The least expensive way is to take the train to Sorrento. From the Naples airport, take the free shuttle to Napoli Centrale Garibaldi Train Station. Go to the lower level and take the Circumvesuviana train to Sorrento which is the last stop. Trains depart every 30/60 minutes and the journey can be up to an hour and a half. Warning: in the summer months the train from Naples to Sorrento is jammed, with standing room only, and not air conditioned! It may be a very unpleasant ride. You can buy your tickets from an automated ticket machine or ticket office.
Tickets: Naples to Sorrento 4.50e each
Important Note: Remember to validate your train ticket before you get on the train! If you don’t, you can be subject to a fine and must purchase another ticket. Also, be aware of pickpockets on the train.
Ferry to Sorrento
The first step is to take the airport shuttle to Naples Beverello Harbor. The shuttle departs every 10 minutes. Once at the harbor, find the Alilauro ticket office to purchase your tickets. The Hydrofoil journey is 40 minutes. Go to Alilauro for ferry times and prices. This is a beautiful way to arrive in Sorrento. Be prepared for a gorgeous view of the cliffs and town above!! Be aware that the ferry pier is on beach level and there is an uphill climb to the hotels. However, if you stay to your left when exiting the marina, you will find an elevator lift to take you up to town (cost 1 euro. Of course, taxis are available or you can walk up and enormous flight of steps.
Note: CASH ONLY! Many people waited on line only to be turned away to find an ATM.
Ferry times: 9am 11am 1pm 3:05pm 5:15pm and 6:25pm – varies during seasons.
Tickets: One way from Naples to Sorrento is 14.10e per person – Luggage is 2.10e per piece.
Private Transfer to Sorrento
In my opinion, the most hassle-free way is via private car transfer from Naples. If you decide on door to door transport, I highly recommend Renato Como Transfers. They will pick you up at the airport arrivals point, and take you directly to your hotel in Sorrento. In addition, if you want to sightsee for a few hours, you can stop in Pompeii or Herculaneum. Your luggage is safely stored in the vehicle. Furthermore, you can also stop for delightful lunch at a cliffside restaurant. Anything you desire they will accommodate.
Whatever option you choose, enjoy getting from Naples to Sorrento. Relish the breathtaking views and appreciate the locals! Of course, when you are on the Amalfi Coast, make your way to Capri, Positano, Ravello and Almafi.