By Train

From the central station in Naples there are trains to Salerno. From there you can use buses to Positano or to the Amalfi Coast.Not recommended

From the central station in Naples there are trains to  Sorrento .It is highly recommended 

If you get by circumvesuviana train and sita bus To positano:

There are several Naples train station,but all trains coming into town stop at either Napoli Centrale or Garibaldi -which are essentially the same place,with Centrale on top of Garibaldi.Stretching in front of this station complex is the vast gritty Piazza Garibaldi.
centrale is the slick,modern main station.it has a small TI ( near track 23),and ATM (Banco di Napoli near track 24),a bookstore(La feltrinelli,near track 24),and baggage check( deposito bagagli,near track 5).Pay WC are down the stairs acrosss from track 13.Shops and eateries are concentrated in the under ground level.
Garibaldi,at the lower level of the Centrale Station complex,is used exclusively by Circumvesuviana train ( TO use to connect to Sorrento or Pompei).

Inside the Station Piazza Garibaldi in Naples down below and take the Circumvesuviana train to Sorrento the trip takes one hour ( there are two types of tickets: the ticket for a single ride and the integrated ticket (TIC) also applies to bus and subway. If you plan to take other means of transport that ask at the ticket office.
The travel time between Naples and Sorrento is 1 hour and 10 minutes. The trains marked with the initials DD does not stop at all stations and arrive in Sorrento in 50 minutes.
The ticket from Naples to Sorrento currently costs 3 Euros and 60.
Sorrento is the last stop on the line.
The Circumvesuviana of Naples Piazza Garibaldi station is located on the lower level of the station, below the one where the high-speed trains arrive.
The Sorrento trains generally depart from platform 3, to access this binary there are no escalators or elevators. Attention to the message on the display that announce the incoming train to be sure to take the train to Sorrento, or else you risk finding yourself in Sarno! ( it's a single train track, look at the display)
At Sorrento station you will find instead the elevator. The station is at the center of Sorrento.
be careful on the train circumvesuviana in the trait Napoli - Pompei there may be pickpockets.Put the cell phone and the money in the pocket in front and keep the bag always close to you In Sorrento outside the circumvesuviana station you can catch a bus for Amalfi,you will be able to board the bus at the train station .You can buy bus tickets at most newsstand and, Tabacchi Stores, unless you already hold a valid ticket from your earlier trip. ( you can not buy the ticket on the sita bus, without a ticket you will takes a fine of 100 Euros)
On the bus,ask the driver to stop you at Bar Internazionale in Positano.The first stop in Positano CHIESA NUOVA AREA
( In Italiano.Per piacere,puo' farci scendere alla primaafermata di Positano Chiesa Nuova VICINO AL BAR INTERNAZIONALE)
( Please,can you let us get off at the first stop in Positano Chiesa Nuova close internazionale bar )

the sita bus times are not precise because of the roads narrow of the Amalfi coast and traffic .
If the sita buses are full the buses drivers do not stop and you stay down '. I recommend you be in advance at the bus stop

The ownwes michele or Fiorella will meet you at the Bar Internazionale ,in Positano along Via Marconi -the main coastal road,to show you the way to the house which is just 50 meters away.It is very important that you make a call or message at least 30 minutes in advance, when you take the bus bus from Sorrento.
Once you arrive in Positano,you will see a one way street that goes to the center of the village ,down towards the sea.The name of this road is Viale Pasitea,and it is really the main road of Positano where cars are allowed.At this intersection you will find Bar Internazionale,on your left.we are sure that you will have a great time at Casa Perla.

An Alternative: Continue on to Salerno
The Freccia Rossa TAV trains go as far as Salerno. You can get off there and take the bus to Amalfi or one of the ferries to Amalfi and Positano. The Molo Concordia pier is located directly opposite the train station in Salerno, so is the easiest to reach. The Molo Manfredi pier is located a few kilometers from the station, so you will need to hire a taxi.

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 https://www.eavsrl.it/web/) operates frequent train services Napoli to Sorrento ( euro 4,50, time 66 minutes)

FAQ - Amalfi Coast Buses
Where do I purchase bus tickets?
Bus tickets are sold at "tabaccherie" (cigarette shops), newspaper stands, and bars and caffés in all the towns along the Amalfi Coast. In Sorrento, there is a ticket booth at the Circumvesuviana station. Tickets CANNOT be purchased on board the bus.
How much does a ticket cost?
There are different types of tickets, prices of which vary according to the geographic area and duration of validity:

COSTIERASITA 24 hours: EUR 10 with unlimited rides on SITA SUD buses between: Agerola, Amalfi, Atrani, Cetara, Conca dei Marini, Furore, Maiori, Massa Lubrense, Meta di Sorrento, Minori, Positano, Piano di Sorrento, Praiano, Ravello, Salerno, Sant’Agnello, Scala, Sorrento, Tramonti, and Vietri sul Mare. You must validate your ticket on your first ride. Tickets are per person and cannot be used by other riders. You must fill in your name and date of birth in the spaces indicated on the ticket.
COSTIERASITA 24 hours: EUR 12 with unlimited rides on SITA SUD buses between the towns listed above and also valid for local buses running in the Comune di Positano via Mobility Amalfi Coast.
For routes to and from other towns and destinations in the region of Campania (Naples, Caserta, Benevento, and Avellino), travellers can use tickets issued by each single bus or transport company, or a combination ticket combining connections with more than one bus or transport company. Request detailed information and prices at the ticket office.
When you purchase your ticket, you can ask for information regarding which ticket is best suited to your travel plans.

Is there always seating on the bus?
Unfortunately, no. During the crowded summer months, the buses are often standing room only.
How will I know which stop to get off at?
The bus drivers announce the main stops; you can ask the driver to announce your stop when you board the bus.
Is there a bus route which runs along the entire length of the Amalfi Coast?
No, the two main routes are Sorrento - Positano - Amalfi and Amalfi - Salerno. So if you would like to ride ride between Positano and Salerno, you will need to change buses in Amalfi.
Is there an alternative public transportation to the bus?
There is no train route which runs along the Amalfi Coast, so the only public transportation by land is the bus. There are also ferry routes which run in the summer, stopping at Sorrento, Positano, Amalfi and Salerno. Ferry tickets are more expensive than bus tickets, but ferries are a very pleasant way to travel the coast.
Where should I sit on the bus to enjoy the view?
From Sorrento south to Positano and Amalfi, sit on the right side of the bus to look over the Mediterranean. When traveling north, sit on the left side.
Can I take my child's stroller or pram on the bus?
Strollers and prams cannot be transported open on the bus; you will need to fold it and store it in the luggage compartment before boarding.
Is there space for luggage on the bus?
Yes, all buses have an ample storage compartment.
Is there a direct bus route from Naples to Positano?
Unfortunately, no. You will need to take the Circumvesuviana train to Sorrento, and then catch the bus to Positano.
The best option for a stress free arrival: book a private transfer.
Do buses run at night?
No, buses stop running at 10pm.