The plaster of paris is like mud and stones that get deposited over leaves or animal remains, but the mud takes millions of years to turn into stone that we see as a fossil. This particular type of fossil is called a cast. Other fossils form when amimal or plant remains are buried in rock, mud, tar, volcanic ash or ice. They all take millions of years to form.
Some fossils are actual remains found in ice, amber tar pits, or sedimentary rocks.