Mushrooms (fungi) require specific conditions for growth. These include temperature, light and humidity. In general, mushrooms prefer dark, cool and moist conditions. These are difficult to control outdoors, so most amateur mushroom growers grow their mushrooms indoors.

A portion of your basement may be suitable, however since most mushroom species prefer cool temperatures (50-60°F) this location may be too warm in summer unless the room has air conditioning (then humidity may be a problem). Growing your mushrooms as a winter project may be the answer.

The best way for a beginner to grow mushrooms is to start with a kit. Kits for various species of edible mushrooms are available from many reliable suppliers.

The North American Mycological Association website has useful information on growing mushrooms and has links to on-line suppliers 

A much more detailed source suitable for non-beginners is this book:

Paul Stamets.Growing Gourmet and Medicinal Mushrooms. 3rd Ed. Ten Speed Press. Berkeley and Toronto. 2000

Courtesy of NYBG Plant Information Service