You can find fossils in Glittering Cave by smashing the cracked rocks with Rock Smash. At first, you’ll only find one type of fossil - Old Amber - but after beating the Elite Four, you’ll start to find a variety of other fossils.
Take these fossils to the Fossil Lab in Ambrette Town and hand them over for them to be converted into Pokémon! Sweet! Below you’ll find a list of all fossil-types and what Pokémon they revive.