Spiders don't need to swing from wall to wall by spinning a web. They can just crawl right up the side and across the ceiling to get where they want to go. It doesn't even matter if the wall is lined with granite or ceramic tile. Spiders can cling to any dry surface.
Spiders have small tufts of hair on their legs that are the base structure for microscopic hairs that allow them to cling to objects. These microscopic hairs, called setules, cover every single hair. They are so small that hundreds of thousands of setules are on each hair. The close spacing of these hairs, their sheer number, and their microscopic size give them the ability to create a molecular reaction that helps the spider walk on any surface.
The setules on a spider's leg don't actually grab the surface. Instead they apply enough force to create a temporary molecular bond. This is referred to as the van der Waals force, a type of molecular bond. To put it in the simplest of terms, the setules are so small and so close together that the molecules of any surface they touch are essentially forced to squeeze between and adhere to the setules. This bond is rather weak and only temporary, allowing the spider to move freely. Of course more complicated actions are at work, but the end result is that the setules create molecular force, which in turn allows a spider to cling to surfaces.
Just a single leg can hold a spider on any surface. In fact, the force generated by one leg is so strong that it could suspend 21 times the spider's weight from a ceiling. When all eight legs are in contact with the surface, the force created could suspend up to 173 times the spider's body weight. This means that the spider needs only a very small point of contact with only a single leg in order to cling to a surface. Of course contact with more legs is necessary to move.
Since the method used to cling to a surface is molecular force, rather than gripping, hooking or grabbing, a spider can stick to any dry surface, whether it is slick or rough. For example, a slippery glass tank keeps most climbing animals and insects near the bottom since it offers nothing to cling to. A spider, however, can walk right up glass, ceramic, polished wood, metal or any other slick surface that might cause other animals to slip.