Naples International Airport Capodichino is located 7 Km northeast of the city centre ,is southern Italy's main airport It's served by a number of major airlines and low cost carriers,including easy Jet ,which operates flights to Naples from London.Paris,Berlin and several other European cities
( tel.081-789.6111 for operator,tel.081-848-888-777 for info,handy info desk just outside baggage claim,https://www.aeroportodinapoli.it/).

Naples is southern Italy's main rail hub.Most national trains arrive at or depart from Stazione Centrale.(Tel 081-554-31-88 :piazza Garibaldi )
or underneath the main station ,from stazione Garibaldi.Some services also stop at Mergellina station National rail company trenitalia Tel 802021:https://www.trenitalia.com/ ) runs regular services to Rome ( 2nd class euro 12 to euro 43.High -speed private rail company Italo tel 06-07-08:https://www.italotreno.it/it
also runs daily services to Rome (2nd class euro 15 to 39,70 minutes ,up to 15 daily ).not all Italo Services stop at Rome Termini with many stopping at Roma Tiburtina instead Circumvesuviana Tel 800 211 388 ww.eavsrl.it) operates frequent train services Napoli to Sorrento ( euro 4,50, time 66 minutes)

From the Capodichino Airport in Naples you can either catch a bus that takes you to sorrento or catch a bus or taxi for the train station in downtown Naples ( Piazza Garibaldi ) .There are buses for Sorrento at the times:9,00,11,30 13,00 14,30 16,30,and 19,30 ( please note: schedule is subject to change without notice;please check Http://www.curreriviaggi.it for any changes ).
If you'll be reaching Sorrento by bus follow these instructions: From Sorrento you can catch a bus for Amalfi.You will be able to board the bus at the train station.
You can buy bus ticket at most newsstands and Tabacchi stores,unless you alredy hold a valid ticket from your earlier train trip.Visit http://www.unicocampania.it for detailson local transportation tickets.on the bus,ask the driver to stop you at Bar Internazionale In Positano.
in Italian you would ask: Per piacere,puo' farci scendere al Bar Internazionale,a Positano?
(Please,can you let us get off at Bar Internazionale ,in Positano?)

From Naples Airport to Naples harbor (Beverello): Shuttle service leaves every 10 minutes ( Alibus shuttle buses zip you from the airport to Naples Centrale train station/Piazza Garibaldi in 10 minutes,and then head to the port/Piazza Municipio for ferry to Capri , Sorrento and Positano( buses run daily 6,30-24,00 )
From Naples harbor in Positano, with stops in Capri: Search times on site Alilauro e Caremar; trying to combine with arrival and departure. Definitely not an inexpensive solution, total costs may reach around 40/50 € per person.