To reach central Rome from Fiumicino airport, take the Express train that departs every 30 minutes to Termini Station (taking around 25 minutes). From there you may take the metro to just about anywhere in the center of the city.
If you fly on a low-cost airline you land at Ciampino Airport. A bus connects the airport to line A of the metro, which takes you to Termini station in the center of the city in about 30 minutes.

If you prefer private transportation from the airports, choose the Fiumicino or Ciampino Private Arrival Transfer and the Fiumicino or Ciampino Private Departure Transfer.
There is also a Fiumicino Airport arrival shuttle and departure shuttle service.

Getting around the city is also fairly easy, as the metro runs to all of the major touristic areas. It is a good idea to invest in the tourist ticket that allows you to use public transport with no limitations for three days. If you're staying for a shorter period, you may opt for the daily ticket, valid until midnight of that day.

To locate any particular street or place, use the map below, and if you plan to go on a tour of Italy, check out these cheap car rental rates.