Free wi-fi

The connection service provides is provided by the Municipality of Prato.
The Municipality of Prato has already activated an extensive Wi-Fi service in the city of Prato [It's the Municipality of Prato, you don't need to repeat the city name] and will gradually extend the covered areas area covered by the service will be extended gradually. [you may want to put a time reference here, if you have such information. Something like "over the course of the next two years", for example. It's not necessary, but I think it would sound better]

How does the sevice service  is working work?
All the citizens can use the service free Wi -Fi, provided they are already registered for the service. To register, you must access the web page[What web page? You could be more specific here],where you will be asked   It is asking for some data, an email adress and ,a phone number of an Italian trader and the following data :

name and surname
sex
date and place of birth
residence address
location
state.

The data, along with the information on the mobile users (the owners of the phone), are is used for statistical purposes along with the information about mobile users (owner of the phone) to enable allow the competent judicial authorities to identify those responsible in case of misuse of the service. and they are:
name and surname
sex
date and place of birth
residence address
location
state
You also must read carefully and explicitly agree to the "Terms of Service", which It is a real contract that stipulates an agreement between the user and the Administration and that will must be comply complied with in all its parts.
When you confirm your registration, a text massage message with containing a password will be sent on to your mobile phone. In order to access the Wi-Fi, you must sign in using that must be used password, along with the same number [what number? Do you mean some sort of username?] when you want to access to Free Wi -Fi.
You can’t  use the same mobile number more than once to register.register more than once with the same mobile number. [Your sentence wasn't wrong, but I think it sounds better this way]

I hope this helped!