transportation from Rome to Siena

Train is easy enough. Take the Leonardo Express to Termini, then connect to Siena, a 3-4 hour trip with one change for 14 to 40 euros depending on the train (AV, IC, Reg) and class. You can research schedules at http://www.trenitalia.com. FWIW, I like the train as an option upon landing in Europe and proceeding to another city because we can nap a bit which helps us get over jet lag. (Personally I can't nap on busses or in cars.) Then when we get to our destination for the night, we can stay awake until a normal bedtime and be morning we feel local.

You'll get different replies and here's mine: I'd take the bus (Sena). It's direct to just outside the main walls whereas the train requires a transfer and the station is more remote. But either way, no need to rent a car.

Bebe, I agree with Laurel in terms of taking the train as it's an easy option from the airport. When you reach the rail station at FCO, you can buy your tickets both for the Leonardo Express and the train to Siena either at the staffed ticket office (cost may be higher) or the automated Kiosks. The trip from the airport to Termini station is about 35 minutes, but be sure to allow yourself enough time to connect to the train to Siena. Check the Trenitalia website to get some idea on the departure times of trains. The Leonardo Express arrives at one of the "far" tracks (Binario 26 as I recall), so with the crowds and being tired, it will take you about 10-minutes to walk to the front of the station and locate your next train. You might allow a bit of extra time to grab a Coffee or whatever. Although the station in Siena is at the bottom of the hill, it's not difficult to get up to the city either via Bus or Taxi. I believe it's now possible to travel up a series of Escalators in the shopping mall across the street from the station, but I haven't tried that personally yet. Happy travels!

Bebe, To me the easiest way would be the bus http://www.sena.it/index_e.htm
because there would be less changes than the train. FM1 http://www.trenitalia.com/cms/v/index.jsp?vgnextoid=240ab31e1bdb7210VgnVCM1000004016f90aRCRD to Tiburtina, walk across the street to the bus then arrive at Piazza Gramsci at the top of the town.

If you decide to take the bus from Rome Tiburtina to Siena, then take the local train from the airport to Tiburtina train station (8 euro), and not the Leonardo Express to Termini and Metro to Tiburtina (15 euro and takes longer). Think Henry has provided a link to the local train schedule in his post.