If you are trying to get oil in New World, you will need to start your search within the swamp regions of the game. In these swamp regions, Weaver's Fen in particular, you can find oil in the form of large black pools of liquid called seeping stone.
You can also find these black pools of liquid in large quantities towards the south of the region known as Weaver's Fen. However, you will need to have a mining skill of at least 20 before you will be able to mine the large pools of oil.
Related: How to respec skills in New World
Luckily, you can raise this mining skill with no problem by mining easier to find resources such as stone and various ore. We also recommend trying to raise the skill to level 45, as you will unlock the ability to track oil at this rank, which will make finding the resource easier.
Once your mining level is around 20, you will be able to get oil. However, if you can't find oil in Weaver's Fen, you can always try the northwestern area near the first light hamlet. But if you still have trouble, the folks over at newworldfans.com have an awesome resource map you can use to locate oil among other resources. That being said, once you got your oil, you will be able to use it in various crafting recipes in the game.