Most people consider Pompeii a side trip from Naples rather than Rome. However, on my first trip to Italy I had a few extra days on my railpass, and decided to use one of them up by taking a day trip to Pompeii from Rome. I caught an early morning train to Naples (about 8:30 am or so) which is about 2-3 hour long ride, then switched in the Naples train station and bought a ticket for the Circumvesuviana train that runs from Naples to Sorrento, stopping at Pompeii along the way. (The Circumvesuviana train is not covered by your rail pass, you'll need an additional ticket for it, in 1998 it cost about $3 each way. The trip from Naples to Pompeii is about 1/2 hour.)
Make sure you get off the train at the Pompei Scavi stop, not the Pompeii stop. (Scavi is the ruins, Pompeii is the modern day city). Entrance to Pompeii was L12,000 (in 1998), and I strongly suggest you rent an audioguide for a good understanding of the ruins if you do not go with an organized tour. You get a detailed map with your ticket, and there is a baggage check near the entrance.
I was completely awestruck by how well things in Pompeii were preserved. There were walls with paintings that looked like they could have been painted just a few hundred years ago, shop counters that were still standing in one piece, marble baths still intact. The audioguide was full of good information, and it was pretty easy to go at whatever pace you chose.
If you get hungry or thirsty while in the ruins, there is an (overpriced) snack shop/cafe near the entrance. It closes a few hours before the ruins actually close - around 3:00 pm if I remember correctly. Hours for the ruins are 8:30 am-7:30 pm Mar-Sept and until 5:00pm Oct-Feb.
I really enjoyed the trip to Pompeii, but I only recommend it as a side trip from Rome if you have railpass days you want to use up. Otherwise do what most people do and see Pompeii as a day trip from Naples or Sorrento.