Flights to Florence are available from major international airports in India. Airlines that operate include Lufthansa, AirFrance, Swiss Air etc. From Florence one can take a bus to Siena. Alternatively one can also take a flight to Rome and travel to Siena by train.
Siena does not have an airport. One has to land at Florence, Rome or Pisa and take a train from there.
Driving around Tuscany will give you the most flexibility with your schedule. It will also give you breathtaking views of the Tuscan countryside. However, gasoline prices in Italy are very high. One must also keep in mind that headlights need to be switched on at all places except city squares. Major rental companies all have offices in cities and airports.
Railways are quite developed in Tuscany and remain one of the easiest and oldest ways of connecting cities. However, Siena sits atop a hill and therefore railways have a bit of a problem. Even though trains are amply provided, the station is at the foot of the hill. One has to take a local bus to go to town or walk uphill to reach the town.
The most convenient way to travel between Rome and Siena or Florence and Siena is by bus. There are two kinds of buses that ply between Florence and Siena-the Rapida(faster) and the Ordinaria (ordinary). The Rapida takes less time, 1 hr 15 minutes, as it travels non-stop. The Ordinaria stops at two villages on the way and therefore takes slightly more time (1 hr 30 minutes).