How to get from Rome to the Amalfi coast?

Train from Roma Termini to Salerno.
(Train schedule: www.trenitalia.com)
From Salerno take a bus to Amalfi
(bus schedule: http://www.sitasudtrasporti.it/public/tpl/campania/5120.pdf)
or, if you prefer, you can also take a boat
(boat schedule: http://www.salernostazionemarittima.it/pages/arrivi-partenze/orari-traghetti-amalfi-e-positano.html#.U8b-3JRdU3c)

It's in the book, but Rick gives it away for free:

http://www.ricksteves.com/watch-read-listen/read/articles/naples-sorrento-and-the-amalfi-coast

Roberto's advice will allow you to avoid the Circumvesuviana, which you should if possible. Lately it's a nightmare.

Zoe, can you elaborate on the Circumvesuviana? I'm just curious what the problem is "lately?" Too packed? Running off schedule?