The University of Pisa is not a campus-based university so it does not have its own dorms. However there are various options available to students to find an accommodation.
The average rent for a single room in a shared apartment is between 300/400 euros a month
Please note that landlords normally ask for a deposit equivalent to one/two months rent upon signing the lease
You are strongly discouraged to pay for a long-term room before you obtain the Visa.
If you want you can first book a short-term room (10 days/ 2 weeks) and then you can look for a long-term accommodation once you are in Pisa.
Short-term rooms bookings can be normally used for Visa purposes
In any case, always make sure to sign an agreement saying that you can have your rent/deposit back if for some reason you are not finally able to come Italy
If you are looking for a student dorm, there are several options available such as Studentato Cappuccini Hall, Casa dello Studente Villa Giulia, I Praticelli Residence, Residence Tulipan, Residence le Benedettine, and Pensionato Toniolo