Barrel tiles, the most common type of ceramic tile, resemble half cylinders about 16 inches long. In the old days they were individually made by hand, their tapered shape achieved by forming the clay over the top of the thigh. Tile roofs are quite heavy, so the roof framing must be stout enough to support the load. Waterproofing is achieved via a waterproof membrane laid directly on the roof sheathing. Then the clay tiles are laid one by one in a pad of mortar. Tiles turned upside down form a trough, which is then covered by tiles laid right side up. The whole process is quite labor intensive, which makes an authentic tile roof quite expensive.
In addition to barrel tiles there are a number of variations of clay roof tiles. Some are shaped like thick shingles, some like slates. A high-quality tile will be hard-fired and will not absorb moisture that could fracture the tile when frozen. All high-quality tile roofs are expensive, both in terms of the material and the installation, yet in the long run the most expensive might be the most cost effective, since you can expect to get 60 to 80 years or even more out of a well installed tile roof.