You use the Mohs hardness scale by testing your unknown mineral against one of these standard minerals. Whichever one scratches the other is harder, and if both scratch each other they are the same hardness. It was devised in 1812 by Friedrich Mohs (so it's never spelled "Moh's") and has been the same ever since, making it the oldest standard scale in geology—and perhaps the most useful single test for identifying and describing minerals.
The Mohs scale is strictly a relative scale, but that's all that anyone needs. In terms of absolute hardness, diamond (hardness 10) actually is four times harder than corundum (hardness 9) and six times harder than topaz (hardness 8). The scale uses half-numbers, but nothing more precise, for in-between hardnesses. For instance, dolomite, which scratches calcite but not fluorite, has a Mohs hardness of 3½ or 3.5.
There are a few handy objects that also help in using this scale. A fingernail is 2½, a penny (actually, any current U.S. coin) is just under 3, a knife blade is 5½, glass is 5½, and a good steel file is 6½. Common sandpaper uses artificial corundum and is hardness 9; garnet paper is 7½.
Mohs hardness is just one aspect of identifying minerals. You also need to consider luster, cleavage, crystalline form, color, and rock type to zero in on an exact identification. See this step-by-step guide to mineral identification to learn more.
A mineral's hardness is a reflection of its molecular structure: the spacing of the various atoms and the strength of the chemical bonds between them. The manufacture of Gorilla Glass used in smartphones, which is nearly hardness 9, is a good example of how this aspect of chemistry is related to hardness. Hardness is also an important consideration in gemstones.
Don't rely on the Mohs scale to test rocks. It is strictly for minerals. The hardness of a rock depends on the exact minerals that make it up, particularly the mineral that cements it together.