Parsley should be kept cold and stored in the refrigerator for maximum freshness. You can add 1 to 2 inches of cold water to a jar and place the parsley (stems down) in the jar like how you would store flowers. Make sure you switch out the water every couple of days, or when the water looks cloudy.  You can also save space by storing cleaned parsley in an airtight container with the parsley covered with a damp paper towel. Using these methods should keep your parsley fresh for up to a week.