Slabs are half-blocks. Upside-down slabs occupy the top half of their block space rather than the bottom half. To place a slab upside-down, right-click on the bottom of a "ceiling" block, which can be removed after the slab has been placed, or by right clicking the top half of the side of another block, if the player wishes to place it on the side of another double or single slab block.
All types of "stone" slab have the same data values; like wood and colored wool, they are differentiated by their damage values: stone slabs have a damage value of 0, sandstone slabs has 1, old wooden slabs has 2 (which were actually stone, and are still obtainable), cobblestone slabs has 3, bricks has 4, stone bricks has 5, and nether bricks has 6. Damage value 7 is occupied by nether quartz, and formerly by a smooth variant of the stone slab. Upside down stone slabs have a damage value of 8, sandstone has 9, wooden has 10, cobblestone has 11, bricks has 12, stone bricks has 13, nether bricks has 14, and nether quartz has 15. Real wood slabs use a different set of block and damage values.