The answer to your question, how to store mushrooms, really depends on where you get your mushrooms. If you get them from supermarkets, then just keep the plastic wrappers intact just like the other answerer said. They can stay fresh in this condition for more than a week. But after opening them you must make sure that you transfer the mushrooms to a “moisture sealed” container as too much or too little moisture can ruin your stash of these tasty fungi.
In my case, I always buy mushrooms directly from a mushroom farm near my area. There is no pre-package, so I find that the easiest way to control moisture around the mushroom is by wrapping them with a paper towel before putting them inside a plastic ziplock or an ordinary plastic bag. Poke a few holes into the plastic bag to let air circulate. What the paper towel does is keep the moisture of the mushrooms inside to prevent them from drying out while at the same time keeping out the moisture from the fridge. Remember, too little moisture can result to dried mushrooms while too much will make them slimy.
Mushrooms packed with paper towel can last much longer than those stored in ordinary plastic bags. In my case, I can keep them inside the crisper for up to two weeks with no worries.