You must go to the registry office at the nearest Local Health Unit (ASL):

You must bring with you the following documents:

Your identity card/passport;
Your Tax Code (self-certified);
The declaration of non-resident status;
The declaration of indigence.

Where to go: Go to the registry office of the nearest Local Health Unit. Here you will be  given a health card in order to receive assistance under the same conditions as Italian citizens (Maps)

How to register to the SSN

When you or your children feel sick

Read more: Useful Links