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.
Visa regulations include applying at the Italian embassy that is the closest to your home. You must have overseas medical insurance in order to qualify for a tourist visa. You also need to show a tour itinerary including a date of return. Italy is also part of the Schengen Area and therefore a Schengen visa would allow you to travel between the 26 countries where Schengen visas are valid.
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 nearest airports to Siena are in Florence, Pisa and Rome. Buses and trains connect Siena to these cities. However, travelling to Siena from Florence is especially easy. Siena is 1 hr 18 min from Florence SMN railway station by train. However, the train trip often requires a break in Impoli and therefore one might consider taking buses from Florence to reach this city. A bus ticket from Florence to Siena costs —6.50-7.00. Buses to Siena are available 2-3 times per hour from Florence.