These are the recommended options from getting to your hotel or into the Rome city center from the airport:

Leonardo Express Train:  the express trains whisks travelers into the central transportation center, Rome Termini station.   From Termini, travelers can catch taxis, busses, or the metro to get to destinations.   A good tip would be to select a hotel within walking distance from the train station.   The train station for the Leonardo Express is located within the airport and is easily walkable.  Follow the "Treni" signs.  Purchase a ticket for about 14 euro, validate it before getting on the train, and you will be in town in about 30 minutes without delays like traffic jams.

Taxi:  Taxis are regulated and charge a flat fee of 48 euros (plus a small fee per piece of luggage) to go from the airport to a hotel within Rome.   Make sure to take a licensed taxi, set the fee before getting into the cab, and never take a ride from someone who solicits you inside the airport.  A taxi ride should be about 45 minutes to an hour, depending upon traffic.

Bus:  The cheapest, but slowest way to go, is the bus.   I like the Terravision bus service (http://www.terravision.eu/airport_transfer/bus-fiumicino-airport-rome/).   It provides cheap (as low as 4 euros per person) and reliable transport into Termini station.   Of course busses run on their schedule, not your, so expect the entire trip, after considering wait time, to be about an hour.

For more information about The Traveling Professor small group tours to Rome and the rest of Italy, see http://www.travelingprofessor.com/