Dirty Fossils drop when mining the following blocks:
Once obtained, these Dirty Fossils can be cleaned by the Archaeologist (/warp fossils) for £50 per Dirty Fossil - in return, you'll receive Clean Fossils.
Clean Fossils are obtained by cleaning Dirty Fossils at the Archaeologist's camp (/warp fossils) and when right-clicked, will give you a random fossil part. There are three parts to each dinosaur fossil species, a skull, torso and tail.
To gain rewards for collecting fossils, you can submit your fossils into your Fossil Collection, which can be accessed via the Archaeologist (/warp fossils). To submit a fossil, click the corresponding icon within the Collection page, this will take the fossil from your inventory and display it within the Collection.
Once a skull, torso and tail have been submitted for a whole species, you can claim a reward by clicking the chest icon to the right of the submission area.