The itinerary starts from the Palazzo Comunale in San Gimignano where on May 7, 1300, Dante Alighieri arrived as the ambassador for the Guelph league. Dante made his speech in the room that's now dedicated to him. Looking up, he saw the same paintings depicting the tournaments of knights and hunting scenes by Azzo di Masetto that we can still admire.
Heading up the stairs, you reach the Podestà's Room that's decorated with the cycle painted by Memmo di Filippuccio at the beginning of the fourteenth century. The scene of the readers could represent Paolo and Francesca's kiss although we do not know if it is actually a kiss due to an abrasion on the fresco. However, "Galeotto has been the book and who wrote it" (Inferno, V).
Once you have seen the Camera del Podestà, it's highly recommended to climb to the top of the Torre Grossa for an unforgettable panorama. At the time of Dante, the tower was still under construction.