Most Inter-city trains arrive at Termini Station. A few trains, particularly those arriving at night, arrive at Tiburtina or Ostiense stations.

Giovanni Paolo II - Termini Station
The hub of Rome's transport system can be confusing when you first arrive, but the following explanations of its layout should help you get oriented. Once you have got off the train and have walked down the platform, you will reach the main gallery. The exit by platform 1 will take you to the north side of Termini; the exit by platform 22 will take you to the south side of Termini. Continuing away from the platforms past the main gallery, you will reach the main hall. Exiting from the main hall you will find Piazza dei Cinquecento, the largest bus terminal in Rome, where the access to the city's two metro (subway) lines, A and B is also located. The night bus to Fiumicino airport stops here as well, although you'll have to look very hard for the sign.
 
 
Below is a list of what you will find - besides trains, buses and metros - at Termini station:

• Luggage Storage
  Open 5.15am - 12.20 am - € 3,10 per 5 hours, per item.
• Alitalia office
  Tickets to the airport can be bought here.
• Police and Carabinieri Station
  If you have lost luggage or documents (or have had them stolen) on the train, report them here.
• Tourist Office
• Eurail and Train Information Office
  English spoken sometimes
• Banks and ATM'S
• Banca S. Paolo di Torino ATM'S
• Ticket offices
• You will also find a pharmacy, an electric appliances store, a travel agency, news stands with international newspapers, and restaurants.
• In all major Italian train stations you will find an office dedicated to facilitating train travel for disabled people. Upon request (which must be made at least 24 hours in advance for Italian trains, or 3 working days for international trains) these centers can arrange transportation for disabled people in the train stations upon departure and arrival. Other services include wheelchair use, luggage transport, and train information.
  Please contact: 064881726 (office located by platform 1) in case you need to arrange services for disabled people in all the stations of Rome.

Note: Remember to validate your ticket before getting on the train. Fines are pretty high!

Tiburtina Station
The second biggest train station in Rome, easily accessible by bus and metro (Line B) from the center. The slower (and cheaper) train and night bus to Fiumicino airport leave from here. Facilities at the station include a 24 hour supermarket and exchange office. Across the piazza in front of the station you will find the buses that depart for destinations all over Italy and abroad. The ticket offices are located in the piazza and around the corner on Circonvallazione Nomentana. From Termini: Line B stop Tiburtina or Bus 492.
From Termini: Line B stop Tiburtina or Bus 492

How to read Italian Train Time-Tables
There are train timetables posted throughout the station. In addition to the immense permanent tables located high above eye-level, there are numerous yellow posters with more extensive and current information. On these yellow posters, you should not check only the "final destination" column. Rather the city you want to reach might also be found in the "principali fermate" (major stops) column or "annotazioni" (notes). The green trains (and some black trains leaving at night) are the normal slower trains, the red trains (IC, EC, EN, and ICN) are faster and require a supplement, while ES (Eurostar) being the fastest of all are even more expensive and require reservations on Saturday and Sunday.

People planning to travel around Italy a lot should consider buying a Kilometric Ticket (Biglietto Chilometrico). This ticket is good for 3000 kilometers of travel within 2 months,it can be divided among up to 5 people and is available for 1st and 2nd class.

Useful web sites:
www.trenitalia.com official railway site
www.romatermini.it