Want to travel to the Amalfi Coast by Train? Hop on a train from Rome Termini Train Station and go to either Naples or Salerno. From there you can jump in a private car transfer (arrange prior) or hop on a bus to your Amalfi Coast destination.
Rome to Naples by train is 1hr 10 - 3hrs (depending on fast train or regular)
Rome to Salerno by train is 1.5hrs - 3hrs (depending on fast train or regular)
The further drive through to Amalfi (town) is 1.5hrs from Naples, or 50mins from Salerno (both approx depending on traffic)
Note: If you are staying at the top end of the coast (Capri, Positano) then Naples station will be closer, and if you're staying further down the Coast (Ravello, Amalfi) Salerno station is closer.