The easiest way to grow mushrooms at home is with a five gallon bucket full of coffee grounds, and some Oyster Mushroom spawn. Spent coffee grounds can almost always be obtained free from a nearby coffee shop. Oyster mushroom spawn can be purchased online from Amazon or from a mushroom lab near you. Detailed instructions for putting together a five gallon mushroom farm can be found http://www.stormthecastle.com/terrarium/how-to-grow-mushrooms.htm
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While the easiest method of growing mushrooms is to start with spawn that has been isolated by a professional mushroom-grower, for a big challenge you can grow mushrooms from store-bought mushrooms by creating an innoculation room and obtaining a sterile culture at home.