Train from Ercolano to Pompeii

According to the Trenitalia website, there are trains about every half hour until after 10 p.m. The Ercolano station is called Portici-Ercolano. The trains are all either 'Metropolitano' or 'Regionale', so you just buy your ticket at the the station (be sure to validate it). They cost 2 euro.

I will assume that you are not interested in moving between the two modern towns but rather between the scavi (ruins and excavations) at each location?

The Circumvesuviana train is a non-national commuter train (railpasses not valid) between Naples and Sorrento which stops at both Ercolano Scavi and Pompeii Scavi (station called Pompei S Villa Misteri) taking just under half an hour for the 11 stops between the two sites.

The train stops a lot, and there are many trains so the timetable is complex and a little complicated.

A simple overview of those stops of usual interest to tourists on that route is at (2017 on the pdf, don't know of any significant changes for 2018 yet):--
http://www.sorrentotourism.com/downloads/1393-Italiano-orario-treni-circumvesuviana-naso-inv-2017.pdf

The full timetable is here:--
http://www.diariopartenopeo.it/orario-circumvesuviana-napoli-sorrento/

Click on the timetable to blow it up, then get out your microscope or click on it again then the blow up icon upper right corner. You may find that the summary above is easier.

To change directions click just under the timetable where it reads "Clicca qui per l'orario della Circumvesuviana da Sorrento a Napoli"

Yup, it is in Italian.

Take a parasol.

Typically, tickets to this train (except at Naples, the main station, with national rail platforms upstairs) are sold by the newstands nearest to the local station. Even at the very busy Sorrento station, there is no rail employee running a ticket office; You go to the newstand just to the right of the entrance. You have to "validate" your ticket in a machine on the way to the platform. Otherwise you're in violation of the ticket rules.

Note that the station in modern Herculaneum is up a steep hill from the historic excavation site - just allow time and energy. About a 15-minute walk, with sidewalks. BTW, most people would not sleep in Ercolano or Pompeii, modern cities. They would sleep in Naples or Sorrento, so as to have more things to do, and restaurants to choose from. Are you staying in Ercolano?

You will be using the Cirumvesuviano train from Ercolano to Pompei Scavi, so there's no need to pre-pruchase tickets. Make sure the train goes to Pompei Scavi, as not all trains from Erclano go there. My recollection is that the trip only takes about 20 minutes. There should be at least 2 trains per hour.

Nigel very kindly provided one version of the Circumvesuviana schedule but I'll throw this one in as well in case it's a tad easier to read:

http://www.sorrentoinsider.com/en/naples-to-sorrento-train-schedule