How should I get from the airport (FCO) to the city center of Siena?
Bebe, I see two options:
Train from FCO to termini (Leonardo Express), change trains to Chiusi, change trains to Siena, then bus or taxi to Siena center. See http://www.trenitalia.com/ Train from FCO to Tiburtina (FM1) walk across the street to the bus terminal and bus to Siena. See http://www.sena.it/index_e.htm
Third option is Leonardo Express to Roma Termini, high-speed train to Florence, and bus (or train) to Siena. It's the most expensive option and a less direct route, but takes about the same amount of time as the slower train via Chiusi.