Oil is an abundant though somewhat difficult resource to harvest in Ark. It is found in the Ocean around the Island. Luckily, there is a reasonable amount in the shallow shores along the coast,in addition to drops from the Trilobite. You can also find numerous Oil Deposits in the Snow Biome above ground, but the harsh weather conditions and dangerous predators can be a deterrent.
There are, at this time, three ways to find Oil. The first and safest is as an uncommon drop from the Trilobite. The second is by finding Oil Gysers underwater. At many locations around the coast of the Island you can find Oil in areas that aren't too deep. You can find large quantites of Oil on the bottom of the Ocean in the Deep areas, too. The third is heading into the Snow Biome where Oil can be found above ground.
Keep in mind that Oil in the Ocean respawns in the same place. So once you know where it is, you can keep returning. It takes time for it to respawn, and so you will have to leave the area for that to happen. The same also appears true for Oil in the Snow Biome.
Harevesting Oil from the Trilobites is probably the first place to start if you just need enough to make a bit of Gasoline or some Oil for your Preserving Bin to make Meat & Prime Meat Jerky. You can harvest enough for crafting. The Trilobites are plentiful enough, and this method of harvesting is less dangerous than venturing into the deeper waters.
If you are planning on harvesting Oil from the Ocean, then there are a few things you can do to make it easier on yourself. First off you should probably look at Oxygen and Stamina when you are leveling up.
Another thing you'll want to use is the Cooking Pot to create Lazarus Chowder. This is one of the Rockwell Recipes that dramatically reduces your Oxygen usage and allows you to regenerate Stamina in the water. This makes life easier all the way around. It is actually very simply to make, assuming you have a few basic Engrams.
Having a Raft can also be of great help. It will allow you to dive straight down and then come straight back up and get out of the water.
This is dangerous. Plain and Simple. You'll need to make sure you are well prepared. That will almost certainly include having a few tamed Megalodons and Scuba Gear. Lazarus Chowder is also highly recomended.
While you can expect to find a lot of Oil, you'll also be running into Megalodons in packs, as well as even bigger and nastier things. Keep in mind as well that right now the only weapons that work under water are the Spear, Pike, and Crossbow.
Harvesting Oil in the Snow Biome is not such an easy task. First the weather itself will kill you slowly, perhaps quickly, if you aren't properly prepared with Fur Armor crafted from Pelts. You also have the dangerous predators of the Snow Biome to contend with.
On the up side, if you have an Ankylo or Ankylosaurus you're in luck. You can use this Dino to quickly and effectively harvest the Oil.