Hi kalena, It is my impression that these folks you speak of are mostly immigranti who are not licensed and are selling knock-offs or Chinese trinkets without paying taxes. I've seen them physically attacked by the local, and legal, venditori in Firenze, seen them pack up their little cardboard table made from boxes and move around the corner whenever the polizia locale or, worse, the Guardia di Finanza, come around. Some use blankets that are easily grabbed by the corners to quickly haul their wares out of sight. These sellers are always keeping an eye out for the official presence, and I've not seen one (ie- the sellers) together with the other (ie- the officials), as far as I can remember. I've witnessed this little dance in many cities over here.
I can always be mistaken, and am never the last word. I am not positive, but without being an EU resident, or having other legal status here, it is possible that you are putting yourself at risk of immediate deportation. And this remains true even with legal status, depending upon your visa, of course. Ultimately, I suspect this is not the life you envision.
On the other hand, if you wish to sell at the various, and particular, mercatini (flea markets, which usually have multiple stalls, as opposed to individual tables set up on the nearest bridge in Venezia, or wherever), then you must register with the local comune as an "obbeista" (not sure I have that word right, but the right word means "hobbyist"). There is a process best checked at your local comune municipio, which will be sure to remind you what your status will allow you to do. Applications to each individual flea market (the same sellers are often found in the various local comunes) probably require individual permits from each comune, I would think (but don't know for certain). One thing is for certain: one cannot just set up a table and sell stuff without one day having to answer questions that were best left unasked. Hope this helps.