When discovered, a fossil comes in the form of a Covered Fossil, and can be put into a Fossil Cleaner to be identified as one of nine different fossils. These cleaned fossils can then be placed into a Fossil Machine to be revived into Pokémon. When placed, it takes up one block of space. It can be retrieved by mining it with a pickaxe.
The Fossil Cleaner does not have to be placed next to a Fossil Machine in order for it to clean fossils. However, the Fossil Machine is still needed to extract the DNA of ancient Pokémon from the cleaned fossils.