Visa

By an "extended stay" I assume you mean longer than the 90 days in 180 you are normally allowed in the Schengen Area as a tourist.
You don't say your nationality, and that will make a difference how easy it is to get a visa. It also depends on the reason you are staying beyond 90 days. Is it tourism (an extended holiday)? Or do you intend to study or work? A work visa will be virtually impossible.

The rules and procedure are listed on this website: http://www.esteri.it/mae/en/ministero/servizi/sportello_info/domandefrequenti/sezione_visti_entrare_in_italia.html
This is the official Italian Government site.

This forum participant is at the end of a one-year stay in Italy and has chosen to extend her stay even further! I follow her on Facebook and she has had a lovely year! I'm sure if you PM her she may be able to give you some advice.

As Chris says, where you are from is a huge factor. What is your current citizenship?

We went through the process last year. For an American wishing to live in Italy on an Elective Residence Visa, we had to prove we had sufficient financial resources, no criminal background, have health insurance, etc. We had to provide letters of reference, an application, have a lease already executed for a residence, and more. We brought about a pound of paper each to the Consulate when we applied. Interestingl.y it took several months to even get an appointment. This site, the Consulate General in San Francisco, is where I took my guidance as we were residents in OR. Where you live and your citizenship makes a difference so if you are a U.S. citizen, look at the site for the Consulate where you live. Note that once you are in Italy, you still have to go through a process to get a Permesso di soggiorno. This has to be renewed annually at first.

Thankyou for your responses. We live in WA state and plan to travel 6 months a year in Italy. We plan on getting an appt at the Italian consolate in San Francisco, but not certain what's required (forms etc) to bring with us or where to find them.

If you are a US citizen, this link has fairly detailed information. Look under the "Resident" section for links to what you need and information about what is required by the Italian government in order to stay in Italy longer than 90 days. There are also financial requirements so that the govt is assured you have enough funds to support yourself...if I recall correctly, you need to prove about $50,000 cash in order for them to approve your stay.

We live in WA state and plan to travel 6 months a year in Italy. We plan on getting an appt at the Italian consolate in San Francisco, but not certain what's required (forms etc) to bring with us or where to find them.

The links provided to you have the info you need. Since you are going to have to go to SF, use their list. You must have a legal lease on a place to live. As to amount of cash required (mentioned above at $50K) they will look at the total income you have from passive sources (i.e., not working in Italy so pensions, Social Security and investments) as well as savings. You may be required to show a roundtrip ticket. Study the website and do everything it says. The lease on a place to live is a huge factor and the first thing they looked at for us. Your FBI background check can take months, so get on that immediately at www.FBI.gov.