Basil can be kept fresh in a jar of fresh water. Clean out a glass jar, and fill it with tepid water, up to 4 inches of the way. Pick your basil from the stems, instead of picking individual leaves. Bring in the stems and dip them in the vase of water immediately. The water should be enough to cover the ends of the stems. If the basil is brought from a grocery store, trim the edges before placing them in the water to increase water retention. Place the water jar in a cool place, shielded from direct sun. It is necessary to change the water daily, so that the basil remains fresh for long.
Another alternative is to freeze your basil. Place the basil leaves on a tray and put it in the freezer for a couple of hours. After this time, place them in air tight containers and put them back in the freezer. Defrost them when you need them in the kitchen.
Milk cartons can also be used to store basil. Clean out the carton, place the leaves inside, and cover it with a zippy bag. It is important to keep the leaves in an air tight environment, to reduce degeneration. Place in the freezer and defrost them when needed.
Basil can also be stored in paste form. It will retain its signature taste and smell for long. Strip the leaves from the basil stem. If you have washed them freshly, pat them dry. Place them in a food processor along with some extra virgin olive oil and salt. Make a puree out of the leaves. The oil will help the basil keep its color, taste and smell. Once done, store the puree in small containers in the freezer and use as and when desired.