The word mushroom is used to refer to the aboveground or reproductive portion of any one of thousands of varieties of fungus; it may or may not have a stem, and is characterized by a cap or umbrella under which are located gills which bear spores. Mushrooms can be edible or poisonous - the latter often colloquially called toadstools - and some poisonous varieties are eaten for their hallucinogenic properties. As Everything2 has enough information already on these so-called magic mushrooms, I will confine my discussion here to mushrooms as a food source.
Thought to have been cultivated since early Greek and Roman times, there are today thousands of varieties of wild and cultivated edible mushrooms that run the gamut of shape, size, and colour.
Perhaps the most common is the cultivated white or button mushroom. Pale in colour with a closed cap, they should be bought only if smooth and unblemished; if bruised or with soft spots or open gills, they are past their prime. The smallest ones have the mildest flavour. A close relative is the cream-coloured cremini mushroom, slightly firmer and more flavourful; if left to mature until the cap is large and the gills are open, cremini become portobello mushrooms, delightfully flavourful and earthy. Other popular mushrooms - many of which grow wild in their homes but are now cultivated for the kitchen abroad - include the shiitake, a flavourful Japanese variety that grows on woody surfaces; maitake and matsutake, Japanese wild mushrooms now cultivated; oyster mushroom, a delicate fan-shaped variety that grows in clumps; the tasty porcini, often sold dried; tiny enoki mushrooms that grow in clusters; and the mysterious straw mushrooms that look kind of like a quail's egg when cleaned.
Wild mushrooms should be picked with great caution because many varieties are poisonous, and not in that wonderful stoned way, but in a death-inducing way. Besides the ones already mentioned, wild varieties include the trumpet-shaped chanterelle, the brain-shaped morel, and the round puffball.
Mushrooms can be sold fresh, canned, or dried. If canned, rinse in warm water first to remove some of the tinny taste. If dried, reconstitute by pouring boiling water over and letting soak till soft.
Fresh mushrooms will keep longest if stored in a paper bag - plastic makes them sweat - or if placed in a single layer on a paper towel and covered with a damp paper towel; in either case, store in the fridge. The end of the stem is generally cut off and discarded before cooking, and because many varieties have a tough stem (e.g. shiitake), it is often discarded altogether. Before using mushrooms, wipe them with a damp paper towel or, if they're really dirty, rinse them in cold water and dry them, but don't soak them as they will absorb water and become mushy. Mushrooms are an amazingly versatile food and can be prepared in practically any way imagineable, so eat 'em, because they're delicious. Yay mushrooms!