You can request your student card if you are in Italy and (in case of non-EU students) after you have applied for the Residency Permit
You will be given the “Studente della Toscana” card and you will be able to use it to access services and facilities of all the universities in Tuscany that are the University of Florence, the University of Siena and the University for Foreign students of Siena
The card may be used, for ex., to eat at the university dining halls, to study in the university libraries and to borrow books there, and also to visit university museums
Moreover, you can use the card to have discounts for museums, public transports, theaters and cultural events
Further info (in italian) here
You can top-up your student card via the Ricarichiamoci website here or by cash through specific ATM machines in the university dining halls
If you want to collect your card you can contact studyabroad@unipi.it