The best way to get to Siena from Florence is to take the bus, not the train. Train tickets are available for about 16 euro R/T from the SITA bus line. The station and ticket office is located about 50 yards to the left of the SMN train station (as you look at it). In fact, here is a map right here: http://www.casa-al-sole.eu/Hauptbahnhof%20Florenz%20zum%20Busbahnhof%20SITA_e.pdf
Here are the sites to see in Siena:
Il Campo: best square in all of Italy. A cafe on the square here is a must for all travelers. Twice each summer, the square is converted into a race track where the wild Palio horse races take place. The Fountain of Joy is the centerpiece of the square. The City Tower overlooks the square and it can be climbed. However, the views from the Museo dell 'Opera e Panorama are much better.
Duomo Museum (Museo dell'Opera e Panorama): If you wish to tour, buy the combo ticket for the cathedral and Santa Maria della Scala. This museum houses the great artworks of the cathedral. Make sure to go upstairs to the back of the room and go up the 131 narrow, corkscrew steps that lead to the Panorama del Facciatone. For me, it is the best view in all of Tuscany.
Duomo Cathedral: Much more beautiful and interesting than the Duomo in Florence, this cathedral houses works of Bernini and Michelangelo. Statues of over 1,000 years of popes spy down from the rafters.
Santa Maria della Scala: Opposite the Duomo, this building was a hospital at one time. It is filled with frescoes and Etruscan works of art. It is worth a visit.
Siena is a walking town. Even I enjoy window shopping here. The main street is Via Bianchi di Sotta. Take your time, relax, and enjoy yourself. We usually spend about 4 hours there.