Herculaneum From Naples?

Select from these options
https://www.rome2rio.com/s/Naples/Herculaneum-Italy

Although I've found Rome2Rio very helpful in years past, today it seems to have been simplified and commercialized. It's also less tutorial for a less-experienced traveler. In this case, using the word Subway to describe the Circumvesuviana commuter train, in a city that has its own Metro trains, is downright confusing.

As is common, the OP has failed to define "best." Fastest, cheapest, most comfortable, most suitable for heavy luggage, best on a super-hot day, most suitable for continuing to Sorrento, most suitable for continuing to the Amalfi Coast? The case of Herculaneum is different from Pompeii, in that the excavation in Herculaneum is a good fifteen minute walk downhill (and then back up .... ) from the Circumvesuviana station, while Pompeii has its luggage check just 100' or so from the Circumvesuviana station. To me, it also matters that Herculaneum has no food insided, except a couple of coin-machines. But it take over an hour to have even the fastest slow-food in Herculaneum-the-modern-city. And you CANNOT re-enter Herculaneum or Pompeii if you go out for food.

It's also less tutorial for a less-experienced traveler. In this case,
using the word Subway to describe the Circumvesuviana commuter train,
in a city that has its own Metro trains, is downright confusing.

Agreed, Tim. Rome2Rio is not always the best tool for figuring transport options, and especially not in this case.

Cheapest way:
You'll want to take the Circumvesuviana commuter train from Napoli Garibaldi station (connected to Centrale) going the direction of Sorrento. Tickets will be very inexpensive, and don't forget to validate them before boarding the train. You'll want to get off at the Ercolano/Scavi stop, and from there it's about a 10-15 minute walk down Via IV Novembre (see a map) to the entrance.

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

The Circumvesuviana line going from Naples to Poggiomarino also stops at Ercolano Scavi, giving you a few more departure options. However, only the Naples to Sorrento line continues on to the Pompei Scavi stop.