After you get your Permesso, you will want to register your residency at your local Comune office. (called Anagrafe) This sets your formal place of residence and you will get an identity card. You will need this for things like buying a car and registering for the national health service.
The procedure is fairly easy. We dropped in our local office and as we are a pretty small comune, they are only open for official stuff a few days a week. The documents necessary for registration are your Permesso, your Passport and a copy of your deed or rental contract showing where you live. You will also need a Marco di Bollo, in our case these were 16eu stamps. You can buy these at many Tabachi. Technically they are supposed to have the police pop by for a verification, but like this will vary from area to area. Some will, some won’t.
Requirements fulfilled, they printed us off a certificate of residence, and told us to come back a week later with passport photos which would be affixed to our Carta d’identita.