You can get a bus to the metro station (Anagnina) from outside the airport for €1 and a metro to the center of rome (Termini) for another €1. The bus is every half-hour I believe.
If there are 3 or 4 or you, it night be worth considering the limo service in the link provided by Ms X - I used it in January and it €35 which I thought was great value to bring you right to you hotel door.
I got the bus in for 8€, and a taxi back for 25 for three of us, we booked the taxi the night before so thats what i advise. picking a taxi up at CIA is supossed to cost 40 -50.
Shane
What are the CIA taxi's. I want to get a reasonable priced taxi to the city centre from Ciampino. Where did you get your's from? Do you think we should ask the hotel we are staying at to book ours?