Ok, i’m no expert, but from my experience living here this is the jist of it:
Some cities (depending on the region and the historical significance of the area) will, as @cprevite already said force you to follow the style of the area to keep the look intact. Tourism is, afterall, one of the most lucrative industries in italy.
You obviously need permits to modify the exterior of your house, especially because you most likely will need to block off part of the road. Most houses face public roads, and you need a permit and advance warning if you need to use them for a protracted period of time.
You also need, and this is in general, a project to be signed by a geometra or architect (“Architetto” in italian, for reference) and approved by the technical office of the Comune (basically city hall, only it sometimes covers more than one small town, our summer home, for instance, is in a very small town that shares its Comune with about 6 others), which is where you should go anyway if you need to know exactly what is allowed and what isn’t as far as renovation goes, before you can actually do any work, which will have to be done by licensed contractors. Also, you can’t make changes to the plumbing, gas and power lines yourselves. You need to hire a licensed company to do the work for you. That kind of infrastructure is very tightly knit in european countries and, therefore, it stands in a delicate balance. The touch of an amateur could end up in huge damage.
(By the way, if you expect to find hardware stores like those you find in the US, prepare to be disappointed. Aside for the fact that italy doesn’t have nough space for such a place to exist on the same scale, save for some areas, it’s just not the kind of stuff we do. Italian cities and towns mostly exist in the same state as they did 100 years ago and, more importantly, are mostly made of interconnected houses, unlike the stereotypical independent two story houses you see in american movies. There is very little room for external modification and, since you need licenses to do most of them anyway, that kind of stuff is generally bought directly by the contractors throught their own channels)
Basically, you can build your own toolshed, a treehouse, small stuff, you can add shelves, you can make furniture, but you can’t mod the house itself without an approved project and outside help.