Much like in the US, you can buy cheese at the deli counter. Near the deli there is usually some already pre-packaged and pre-weighed cheeses for you to browse as well.
Personally, I like my cheese fresh cut, so I recommend going to the deli versus buying it pre-packaged.
Alternatively you can get cheese from a caseificio, which is a shop that specializes in dairy products. These shops are usually close to the farm where the sheep / cows are bred.