Rome to Pompeii Day trip

No need to purchase in advance, although if you do you might save some money if you can secure some Economy or Supereconomy tickets. Those discounted tickets however come with strings attached (I.e. Restrictions) therefore you need to be aware of that. The main restriction is that discounted tickets, once booked, cannot be refunded or changed if later you change your mind and decide to change your travel plans and decide to go at a different time than you originally booked or cancel your trip to Pompeii altogether.
If you are not sure about your plans, you may want to pay full price (base price) and buy the tickets on the spot the day of departure or a day or two prior. If you buy the day before, for example, and pay the "base" (I.e. Full) price, you can always change your reserved train and seats, as long as you do prior to the train departure. I usually buy train tickets on the spot and pay full price. The chance of a train being sold out is almost zero. At most the second class (sometimes called "Standard") is all booked. In that case you can buy a higher class ticket or, if you aren't willing to pay the extra money, wait for the next available train which will have available second class (or standard Class tickets) half hour later.

The route is:
1- Rome Termini to Napoli Centrale station with a high speed train
2-Once in Naples you follow directions to the Circumvesuviana trains. These are commuter trains that depart from the same station ( but from the underground station in Naples). Once you purchase the Circumvesuviana tickets go downstairs and look for trains going to Sorrento (the last station on that line). You will get off at Pompei-Villa dei Misteri station.
Do the reverse on your way back to Rome. The last high speed train departs from Napoli Centrale at about 7:30pm. After that only slower trains are available.
Train schedules below:
www.trenitalia.com (train schedules Rome to Napoli and vice versa)
www.eavsrl.it (train schedule for Circumvesuviana train from Naples to Pompeii and back).
The one way trip from Rome to Pompeii is about a couple of hours.