In Florence you can take the bus in front of Santa Maria Novella railway station.
To reach San Gimignano you will have to change bus in Poggibonsi, from the same place where you will arrive.
I attached a file with timetables (round trip).
From Florence to Poggibonsi, you can see: “FIRENZE – POGGIBONSI – COLLE VAL D’ELSA – SIENA (CORSE ORDINARIE)”
From Poggibonsi to San Gimignano, you can see: “POGGIBONSI – ULIGNANO – SAN GIMIGNANO”
I also attached the legend.
For sunday you have to check: no symbol, holy cross symbol, “SAB E FEST”.