Unlike some of our other plants that we eat from through the season and then harvest for storing all at once (basil), green beans are so prolific, if you don't pick them every day, you'll end up with very large, untasty green beans and basically waste the harvest. In this way, they're a bit more maintenance.
Since I have difficulty eating the same food every day, I'll pick a meals worth and store it immediately. I use the popular blanching method. I don't clip the ends of the beans before I store them. It's a general rule that the less you can mess with a crop before storing, the better.
Lightly rinse the green beans, bring a pot of water to boil on the stove, have a bowl of ice water standing by. Throw the beans in the boiling water for 1 to 3 minutes then strain them and plunge them into the ice water. The cold stops the cooking process immediately. Put them in a container in the fridge for use later in the week. Or to freeze: lay them out on a cookie sheet to dry and try to spread them evenly so there isn't much overlap. You can put the cookie sheet in the freezer so they freeze individually and then you can put them all in a bag or jar together. This way, they don't freeze together and you end up with a clumpy mess. If you don't blanch them immediately, they won't be fresh for long!