My mother is american resident in U.S. I'm italian. How long should I wait to get permission to live in U.S.through sponsorship?

It depend on how old you are and how long your mother has been a permanent resident. We need these facts to make the determination according to the current visa bulletin. Please retain counsel to carefully consider all of your facts and circumstances.

I agree. You should look into your mothers naturalization ASAP.

It depends on how long it takes for your priority date to become current. The movement of priority dates cannot be predicted.

Your mother can petition for you now, but due to quota backlogs, it will take years for you to become a permanent resident. This will hold true even if your mother becomes a U.S. citizen, though that will speed things up considerably. You should consult with an experienced immigration attorney who can explain these options to you as well as review the facts of the case to possibly provide you with better alternatives.

The time you will have to wait will depend on more details such as your age. It will likely take a few years so it is important to begin the process now. I would be happy to talk to you about this if you would like to call for a consultation. buona fortuna!