Pompei can be easily reached by the local Circumvesuviana Train from Naples. You can take the train from Naples's central station and the trip takes approximately 30 minutes. The train station in Pompei is within walking distance to the ruins.
I still don't know exactly where the 2nd train station in Pompeii is, I think I did find it eventually, but I actually can't remember because I think I was out of my mind at the time. I had to get to the Amalfi Coast and the trains didn't leave from the main station, but from some other one, the circumvesuvius station I believe, that was in BFE. I walked for miles and miles until I was probably in the outskirts of Naples, had to turn around, come back, go up some hills, and then I finally found the station, I think, or maybe I gave up. Just be careful and get a map. Getting to Pompeii is easy and cheap, just get to Naples and work from there.
We visited Pompeii on a day trip form Sorrento, which is about 30 km away and easily reachable by train. One can also easily visit Pompeii from Naples (about 30 km) and Rome to the north (about two hours). Sorrento served as our home base from where we also visited the beautiful Amalfi Coast towns of Amalfi and Ravello. See my Italy page for the full Itinerary.
Neither my guidebook nor the nice lady at the train station in Napoli would make this clear, and though it wasn' t difficult to figure out, we were tense the whole way, not knowing what would happen next, on our way to the ruins of Pompei.
Take the Circumvesuviana (a regional train system that goes around Mount Vesuvio) in Napoli, to Sarno or Sorrento. You want to get off at POMPEI **or** POMPEI SCAVI. Both are fine: you can either start in one and return from the other, or the other way around.
If you get off at POMPEI, you'll step right into downtown of modern Pompei, which is quite neat. Then you make a right when you get to the church and start looking for the entrance of the ruins.
But if you get off at POMPEI SCAVI, then you will immediately see the entrance to Ancient Pompei, and finish your visit in modern-day Pompei.