How does mud turn into a fossil?

To become a rock, mud must first undergo the process of lithification. This would involve the subsequent covering of the mud with additional sediments. If the weight of those sediments becomes great enough, the pressure will squeeze out the air and water from between the small clay and silt particles that the mud is composed of. Eventually, minerals will precipitate out of the remaining water, crystallizing to form a cement that holds the clay and silt particles together as a new sedimentary rock.