Preserved remains of once-living creatures can be found buried underground in New Horizons. Every day 4 fossils spawn randomly on your island, but you can only have a maximum six at a time, so it's best to dig up any fossils to allow new ones to be available the next day.
Fossils appear as star-shaped cracks in the ground which can be dug up with a shovel. However, these fossils are unidentified (selling for 100 bells each) and must be assessed by Blathers to identify the fossil name/s and price/s. Be warned; Blathers offers to give a rather-long factual presentation about each fossil if you donate them individually!
The table below shows the fossil names, sale price once identified, and images of each fossil piece;