If you want your fresh broccoli to last as long as possible, you have two options here. The first option is to wrap the whole head in a damp paper towel, and store it in the coldest part of your refrigerator (don't cover it in plastic wrap or a bag). The other way you can store it is in a glass of water just like a bouquet of flowers. Slice of a little bit of the bottom of the stalk so all the dried up part is gone, pop it in a glass of water, and store it in the fridge. Know that if you buy broccoli already cut up, you should use it within a few days tops, no matter how you store it, because it won't last long!