Train from Rome to Pompeii

There is no "exact" price. It depends, as you already suspect, on what trains are you using, time/date of departure, whether you make an advanced purchase, which of the railways you use between Roma and Napoli (Italo or Trenitalia) etc. Regional crap trains, possible without a/c, can take up to 2h extra travel time depending on the route they take.

It takes 1 hour 10 minutes on the fast train from Rome Termini to Naples Centrale train station. From there you'll need to walk downstairs and transfer to the local Circumvesuviana train and travel to the Pompeii Scavi stop. That journey lasts about 45 minutes to an hour. There is another Pompeii stop other than the Scavi...you want the Scavi because that's where the ruins are. Pricing on the fast train from Rome to Naples depends on how far in advance you purchase. I just looked at September 18, 2012 for an example and I see the price ranges from Super Economy Price of 9Euro to a Base Price of 43 Euro (each way). The Circumvesuviana Price is negligible...2 or 3 Euro. There are other slower trains from Rome to Naples which take about 2 hours 15 minutes or so.

Where did you find the fast train price with the super economy I have looked before on rail sites and only seen 1st and 2nd class and it usually says N/A and that is for a week in advance. How long in advance can you buy tickets? Do I need to take the train from Rome airport to central terminal or is there a direct from the airport?

To get the cheapest available fare on a high-speed train from Rome to Naples, book up to 120 days in advance at trenitalia.com. While it's possible to book without registering on the site, things will go more smoothly if you do. You will need to take either the Leonardo Express train or a shuttle bus from FCO to Roma Termini, Rome's main station. Super Economy and other discount fare tickets are non-exchangeable and non-refundable. If you miss your train from Roma Termini to Napoli Centrale, your ticket will be worthless. You have two options: 1. Buy a full fare ticket at the train station at FCO when you buy your ticket for the Leonardo Express. 2. To allow for a possible late flight, leave plenty of connection time by booking a discount fare ticket for a departure time from Termini four hours after your scheduled arrival at FCO.

Can I add a bit to Tim's answer? You can't get a Super Economy fare from FCO to Pompeii. Your trip, if completed all by train, would consist of the Leonardo Express from FCO to Roma Termini Station, a train from Roma Termini to Napoli (Naples), and a third train from Napoli to Pompeii (Pompei Scavi, I think, having been on the Circumvesuviana but not to that stop). The first and third train have set prices which do not change. The middle one, the fast train from Roma to Napoli, has various prices depending on when the ticket is bought and how fast the cheap ones sell out. It is for that segment that you may be able to obtain Super Economy or Economy, the closer to 120 days before travel the better. Your total cost will be sum of trains 1, 2, and 3, and then the return if you are making a return to Rome.