With the entry into force of the Decree nr. 30 dated February 6th 2007 regarding the "Application of the Directive 2004/38/CE about the right of EU citizens and their relatives to freely circulate and stay in the Member States" you are allowed to move without restrictions throughout Italy without applying for a stay permit.
During your first 3 months of stay you have no requirements to fulfil, provided you have a valid identity document. After 90 days of uninterrupted stay in Italy, you have to register at the Municipality of the town where you have your domicile (Comune di Firenze - "Ufficio Anagrafe").
Non EU citizens need to apply for a study VISA before leaving their home country. Application should be submitted at the nearest Italian Embassy or Consulate in your home Country.
If you are planning to stay in Italy for more than 3 months, you have to apply for the residence permit within 8 days from your arrival in Italy taking and filling the form at the post office.
You can renew your residence permit from 90 days before it expires (biennial type) till 60 days after the expiry date (annual type).
Healthcare is very important: it may happen that you will need medical assistance and, if you are not in possession of any appropriate documents, medical assistance can be very expensive. Health card is issued by the official body responsible for healthcare in your Country (AOK, etc.).
For students from other Countries there are no official treaties ruling health care apart from national legislation: if this is your case, you must take out an international insurance which covers costs related to medical treatment and admission to hospital. Nevertheless, in order to avoid problems it is advisable to contact insurance agencies before leaving for Italy. An insurance policy is compulsory if you apply for a residence permit.
*The Tax Code is a compulsory document if you wish to open an account with an Italian bank. This card is issued by the Ufficio Anagrafe Tributaria under presentation of a valid identity document: the card contains a code made up of letters and numbers which makes identification easier in the case of any tax control.