Select plump firm and solid mushrooms. Avoid the limp or dried looking ones. They should not be shriveled or slippery (which indicates decomposition). The mushroom should have a nice earthy smell.
Remove the mushrooms from any wrapping and spread on a tray and cover with paper toweling. Don't moisten the toweling or the mushrooms and place them in the refrigerator in an area that allows the air to circulate. Avoid placing any other items on top of them. The mushrooms should keep about 5 - 6 days.
Cooked Portabellas can be frozen and will keep for several months. Place in freezer containers or bags, excluding as much air as possible. (Uncooked mushrooms don't freeze well.)