How do I find oil?

Walk around the main world and keep right-clicking the oil resonator. It will inform you if there is any oil below you. Note that the oil is randomly spread out around map!

Where are the oil recipes?

They are in the recipes tab, under Electricity and Oil.

How does extraction work?

Once you find oil through the oil resonator, you should get permission from the government to be able to build there if the land is government-owned. If it was private property, contact the landlord, and if it was public, unclaimed land, you may get extracting right away!
Now that that's sorted, place down an extractor right above an oil deposit. ( Note that it does not have to be touching the oil. It works as long as there is oil directly under it. )
Every 599 seconds, even if the chunk isn't loaded ( even if you are offline), you will get 1 oil.
Then you smelt it into LQ and go on from there, using the recipes shown in the recipes tab.