Fake butter (called margarine) is a bunch of tiny water droplets surrounded by a continuous coating of fat. Just like butter. But the fat in this case comes from plants instead of a cow. Some early margarines used fat from beef, seals, whales, and fish, but modern margarine is mostly plant based. Some butter substitutes mix in some cream from cows to make it taste more like butter.
Like butter, the emulsifying agent is milk proteins. Vegetable fats tend to be unsaturated to some degree, and thus have low melting points, making them oils. To raise the melting point, the oils are saturated with hydrogen using catalysts. This is called hydrogenation, and the result is hydrogenated vegetable oil.
Partially hydrogenated vegetable oils used to be used in margarine and butter substitutes, but when oils are heated in the process of hydrogenating, some harmful trans fats are produced. If the fat is fully hydrogenated, so that every carbon atom has the maximum number of hydrogens, then there is no trans fat. Fully hydrogenated (saturated) fats are now used, mixed with oils to get the proper hardness and softening range.
Other emulsifiers, such as lecithin, are sometimes used along with the skim milk. Colors are added (usually annatto or carotene) to get the right yellow color (uncolored margarine is white).
Sometimes the milk is cultured with yogurt bacteria to get a stronger buttery flavor.
Some spreads are a mixture of margarine and butter, to get the flavor people like.