How do people remove the oil from the earth, and how do they process it afterwards?

Answer 1

Typically steam or water is forced down into another well, and thus oil is forced up.

Crude Oil contains a mixture of various products - kerosene and various grades of gasoline. Each has a slightly different boiling point. The crude is heated slowly, and various parts (fractions) are collected at each point. This is fractional distillation

"Sweet crude" has more of the high-value fractions.

Answer 2

It's called fractional distillation - the trade term is cracking. You can look that up.