train from airport rome to rome

The train station is well marked. Just follow the signs. The Leonard Express is non stop from the airport to Termini so you would have to get to your hotel from Termini via local transit or taxi. Have no idea where your hotel is but it is possible that the local train to Trastevere might be closer. Ask you hotel for recommendations.

Ditto what Frank said. Train station at the airport is well labeled. Buy a ticket from one of the small shops near the track and remember to stamp your ticket before getting on. The fines are hefty if you don't. The train will take you to the main train station in Rome. From there you can either take a taxi or ask your hotel which bus or metro comes closest. I found the train very easy and efficient.

Liz, I'd recommend the Leonardo Express as it's an easy 35-minute trip and not affected by traffic. I've found that the cost is €14 PP if you buy tickets at the Kiosk, or €15 PP if you buy from the ticket office. Note that the Leonardo Express arrives at Termini on Track 24 (as I recall) so it's about a 10-minute walk to the front of the station. From Termini you could either use the Metro as Tim suggested or take a Taxi (that's the method I normally use, as it's easier than negotiating the Metro with luggage). As mentioned in previous replies, BE SURE to validate your ticket for the Leonardo Express in the yellow machines prior to boarding the train, or you could face hefty fines which will be collected on the spot! It won't matter if you don't have Euros to pay the fine, most of the Conductors are carrying portable debit / credit card Terminals these days, so the fine will be out of your account before you even get off the train! You may find it helpful to have a look at This Website which has an excellent description of the trip from FCO into Rome. Happy travels!

ATAC is Rome's public transit system. If you go on their website, you can enter in Stazione Termini as the departure point and the address of your hotel as the arrival point and it will tell you how to get there. Also, you can switch the website from Italian to English in the top right hand corner. Also double cehck the spelling of the street name because when I entered in the address it told me it was incorrect (is there perhaps only on "L" in Aurelio?) Anyways, I used Via Marco Aurelio and it looks relatively easy if this is the correct street. It seems like it is right be the Colosseum so if you get lost there will be plenty of Italians around to help you out. Here is ATAC's website:
http://www.atac.roma.it/

The fastest route would be to take the Leonardo Express from the airport to Termini. From Termini take Metro line B two stops to Colosseo. Here's a quote from the hotel site: "To get to the Hotel Romance Rome take the Metro on Line B and get off at the Colosseum and turn left once you leave the Metro station. Cross the road to Piazza del Colosseo and walk around the Colosseum clockwise. Once you arrive at the crossing cross the road again. Via Marco Aurelio is parallel to Via Capo d'Africa and Via Annia." The fare for the Leonardo Express is €14.00. Trains run every 30 minutes and the ride takes 32 minutes. If you want to save some money, take either the SITBusShuttle (€8.00) or a Terravision bus (€4.00) from the airport to Termini. Both buses run every 30 minutes and the ride takes just under one hour.