Sedimentary rocks are types of rock that are formed by the deposition and subsequent cementation of that material at the Earth's surface and within bodies of water
Clastic: your basic sedimentary rock. Clastic sedimentary rocks are accumulations of clasts: little pieces of broken up rock which have piled up and been "lithified" by compaction and cementation.
Chemical: many of these form when standing water evaporates, leaving dissolved minerals behind. These are very common in arid lands, where seasonal "playa lakes" occur in closed depressions. Thick deposits of salt and gypsum can form due to repeated flooding and evaporation over long periods of time.
Organic: any accumulation of sedimentary debris caused by organic processes. Many animals use calcium for shells, bones, and teeth. These bits of calcium can pile up on the seafloor and accumulate into a thick enough layer to form an "organic" sedimentary rock.
Metamorphic: The metamorphics get their name from "meta" (change) and "morph" (form). Any rock can become a metamorphic rock. All that is required is for the rock to be moved into an environment in which the minerals which make up the rock become unstable and out of equilibrium with the new environmental conditions. In most cases, this involves burial which leads to a rise in temperature and pressure. The metamorphic changes in the minerals always move in a direction designed to restore equilibrium. Common metamorphic rocks include slate, schist, gneiss, and marble.
Igneous: Igneous rocks are crystalline solids which form directly from the cooling of magma. This is an exothermic process (it loses heat) and involves a phase change from the liquid to the solid state. The earth is made of igneous rock - at least at the surface where our planet is exposed to the coldness of space. Igneous rocks are given names based upon two things: composition (what they are made of) and texture (how big the crystals are).