There are a number of halachic considerations regarding ripping writing paper, toilet paper, aluminum foil, etc., on Shabbos. There is a discussion in halacha whether such ripping falls under the category of koreia, the prohibition of tearing on Shabbos. According to the Alter Rebbe, koreia only applies to something like a garment which is comprised of various parts that have been sewn together. It is not considered koreia to rip something which has been formed into one entity, such as paper. Therefore, it is permitted to rip such an item on Shabbos. Nonetheless, a person has to make sure not to rip something to a particular size, because doing that would involve the melacha of mechatech, the prohibition of cutting to size on Shabbos. Even if a person is not cutting to size, but wishes to rip paper to fashion a useful item out of it, for example ripping a piece of toilet paper from a roll from a roll in order to have a useable piece of toilet paper, or ripping a piece of aluminum foil needed to cover something, it may not be done on Shabbos. However, opening a package of napkins by ripping off the plastic wrapper, if one does not wish to reuse that plastic, is not a problem. Separating two pieces of paper stuck to each other is, of course, an issur of koreia.