It will be important to first pick your cucumbers when they are about six inches long and keep them in a cool place that does not exceed 40 degrees. You will want to keep in mind that it is important not to store cucumbers along with apples or tomatoes. After about a week in the refrigerator, your cucumbers will start to spoil.
The way in which you go about storing them is extremely crucial with regards to how long they will keep, so you will definitely want to keep that in mind. As long as they are kept in a sealed and cool place, you should be able to get at least one week out of them before they start to go bad and are no longer edible.