Travel to San Gimigiano from Florence

The SITA bus website indicates that you can pick up the bus at the terminal near the S. M. Novella train station in Florence. You will need to transfer at Poggibonsi.

This is the sort of information you can find in Rick's guide books. He's very good at providing logistical information like that.

If you're looking out the side door of the train station, you'll see McDonalds Restaurant. The buses line up to the right around the corner and on the block behind McDonalds.
Another source for a ride to San Gimignano is to take a tour in a shuttle bus down there.

If you can get to the Poggibonsi train station you can jump the local train to SMN ferroviaria stazione.

You need to take the bus from the bus station on Via Santa Caterina da Siena, near the Florence SMN train station. The bus station is on the Bar Deanna side of the station. Every Florentine will point you to the right direction if you say Bar Deanna. People only know how to point you to the Via Alamanni, Bar Deanna, Piazza dell'Unità, Piazza Adua. Those are the cardinal points from the station. The words North, South, East and West will confuse people, don't use them.

You will need two buses.
131 Ordinaria to Poggibonsi, then 130 to San Gimignano.
Schedules below.
http://www.tiemmespa.it

I'd choose to ride the local buses instead of signing on for a tour. It will be a fun adventure and you'll be riding with the locals who depend on the buses.

We rode the bus from Greve to Florence and back and were the only tourists both directions. There were some English speaking locals who were very helpful and fun to talk to. Traveling low to the ground like this gives you a better appreciation of the country.

I hope you have a wonderful, fun filled trip!