Mostly from vegetable seeds, either by pressing or chemical extraction of foodstuffs like soyabeans or corn and some is obtained from nuts (like peanuts for example).
Oil seed pressers are commonly used in developing countries, but many oils are gained from hydrogenated and chemical extraction (soy and corn for instance). Mechanical extraction is used for producing olive oil, but I was quite horrified by reading the link below, as it shows that some oils are produced from crude oil. http://en.wikipedia.org/wiki/Vegetable_oil