Igneous: Igneous rocks form from the cooling and solidification of magma or lava. There are two types of Igneous rocks intrusive and extrusive. Intrusive is formed inside the Earth while extrusive is formed on the surface of the Earth.
Metamorphic: Metamorphic rocks form from extreme heat and pressure. There are two types of Metamorphic rocks, foliated and nonfoliated. Foliated rocks have distinct layers and bands while nonfoliated does not.
Sedimentary: Sedimentary rocks are formed by compacting and cementation of sediments. There are three types of sedimentary rocks detrital, and chemical.
Igneous rocks can be made of any type of rock. If a rock is melted in can be then solidified and cooled to form an Igneous rock.
Metamorphic rocks can be made directly from Igneous and Sedimentary rocks by extreme heat and pressure.
Sedimentary rocks can can't directly be formed by a different type of rock. Igneous has to weather and erode to become sediment so it can compact and cement to become Sedimentary rocks. Metamorphic rocks has to do the exact same thing that Igneous rocks have to do to become Sedimentary rocks.