There are 4 different fossils in Pokémon Sword and Shield and it's possible to combine them in different ways to obtain a Dino Pokémon.
List of the compatibles sets of fossils
Where and how to restore them?
You have to go to Route 6, just before Stow-on-Side. At the top left, you will find a camping tent. A little further to the left, you will find the Professor who can combine your Fossils and give you a Pokémon in exchange.
Where to find Fossils?
The first two Fossils you can easily find are on Route 6, just before the Professor.
When you enter Stow-on-Side, an NPC in the Pokémon Centre will give you 2 more Fossils!
It is also possible to obtain fossils thanks to the Digging Duo (Wild Area, near the Daycare Center). By paying them 500 Watts, they can search the ground for Treasures and you will have a chance to get Fossils.
For the moment, this is the only known way to obtain Fossils. The 4 fossils obtained will allow you to make 2 combinations and obtain 2 Pokémon.