The first Italian census was taken in 1871, with new censuses taken each successive decade. The censuses taken from 1871-1901 are inconsistent from region to region, and usually only name the head of household, his/her occupation, and the number of people living in the household.
In point of fact, there is another version of this site which is in some ways more useful and in other ways less so. I fear that the plan is to make this other site the official one.
Visit http://poster.beniculturali.it/poster/action.do (you'll need to create a new account; I used the same name and password as on the old one for convenience); click the "People" icon to reach the area which is much the same as the older site. Search as usual, click one of the names in the results list, and then click "Vedi atto" to see the record as it is presented in the old site. The major disadvantage I see compared to the old site is that you do not have access to the "Citations" link of cross-referenced documents.
Back at the front page, click the "Places" icon. Enter the name of a comune of interest and click Submit. On the results page, click the name of the comune and then click the "View people associated with this term" link to see a list of all the names referenced (born in? it's not entirely clear) in that comune. This can be a real help when surname spelling varies, is uncertain, or simply mis-transcribed. I find this to be a great tool which is not present at the old site.
My hobby is finding things. Having found most of my own, I am happy to help others find theirs. PM me!