Mushrooms can be grown in sterilized sawdust, boiled straw or used sterilized coffee grounds, depending on what's available in your area. You need to sterile the growing medium and some mushrooms spawn. Some types of mushrooms can be grown by drilling holes in logs and filling the holes with the mushroom spawn. The straw method can be done in a plastic bag - no logs required. Just buy the type of spawn that will grow in the medium you select.
If this is your fist time growing mushrooms why not start with a kit so you can be sure of the type of mushrooms.