I've been getting this question a lot lately so I thought it best to post the answer here.
It is ideal to drink your green smoothie upon having the blades of your blender stop. But as we are all aware, we can't always take advantage of what's ideal.
In general I recommend that you do not make more green smoothie than you will drink in a day. It's quite common that I make a blender full in the morning, drink some and take the rest with me to enjoy the rest of the day.
You don't want to store your smoothie in the blender container, since most containers these days are plastic and you want to clean it as soon as possible. Pour your smoothie in glass containers that have an airtight lid; mason/canning jars work great. Glass is the best substance for storage since it contains no evil out gassing and doesn't impart any odor or flavor. You want the container to be airtight to keep other airborne things from entering your smoothie as well as to minimize oxidation.
With your green love in jars you are good to go for up to 3 days stored in the fridge. Just remember to shake that jar good before pouring that goodness as it will separate a bit while it sits.
Remember... while freshest is bestest, a day old green smoothie is better than no green smoothie at all.