Steam distillation is just what it sounds like. One gets a still - basically two sealed vessels connected by some tubing - with water and plant matter in one vessel, ice or cold water around the tubing, and the second vessel lower than the first. Heat the first vessel till the water boils, the steam goes through the tubing, condenses, and is collected in the second. The essential oil floats on top of the collected water. This is the prefered method for most of the flower oils. A nice byproduct of this is that you get a hydrosol - there is enough essential oil mixed in with the water to scent it. Hydrosols are great to spritz a little oil around the house, or onto your body. Steam distillation is the oldest method of obtaining the essential oils, and was probably discovered Arabia, Persia, or Egypt, and dates back to, well, really long ago.

Cold pressing again, is pretty much what it sounds like. You get two heavy things and squish the plant matter between them, collecting the oil & juice that runs off. Again, the oil usually floats. This is particularly efficient with plant matter that has a lot of essential oil in it - like citrus peels and certain types of leaves.

Fat absorption is the most time consuming of the distillation methods. One takes trays of vegitable or animal fat, lay the plant matter on the fat, leave it for a long time, then replace the plant matter and repeat the process until the fat is saturated with fragrance. The oil can then be washed out of the fat - or rather, the fat is disolved away from the oil. This is prefered for the most delicate of flowers, like jasmine. There are a few drawbacks to this method, as a very large amount of plant matter to make a very small amount of oil, and most of the work is done by hand. As a result, only the oils that cannot be extracted in any other way are produced in this manner.

Chemical distillation is basically a waste of time. Alright, maybe I'm being a little to hard on it. It's fine for fragrance type oils, especially ones to use in a room. Here's how it works: you get some harsh chemical, like turpentine, and use it to break down the plant matter until it releases the essential oil, then youextract the oil from the chemical. You don't always get all the chemical out of the oil, and you can only use it for the stronger oils. It frequently affects the scent, taste, and healing abilities of the oils. It is, however, the cheapest and fastest method to extract the oils.