Hydroponic basil is the same as any other kind of basil, except that it is grown without using any soil. This means the leaves are usually cleaner and don't need much washing before use, since there is never any dirt on them. The other big difference you'll notice is that hydroponic basil is sold with the roots left intact, which is not done with soil-grown basil. However it was grown, the care for hydroponic basil is much the same as the care for any other kind of basil.
Check the basil before you buy it. If it is too dried out it won't keep well, and you shouldn't buy it. If the leaves are soft, supple and well-hydrated, you should be able to store it much longer.
Store basil in the refrigerator, ideally at a temperature of between 40 and 45 F, if you only need to keep it for a week or so. If the basil gets much colder than that it will become black and slimy, and you will have to throw it away. Leave it in the original packaging and place it in the produce drawer. It will begin to lose quality after anywhere from two to seven days, so if you want to keep your basil around longer than a week, skip this step and move on to the next one.
Fill a glass or a small vase with water. It should be large enough to easily support the amount of basil you have. Plain tap water is fine. You don't need any special preservatives or additives for this.
Rinse the basil's root ball in clear, running water that is about room temperature. This removes any deposits or film that might have developed after the hydroponic basil was harvested.
Place the basil in the vase. If there are leaves close to the root ball, remove them before putting the basil down into the water. You should not have any leaves in the water, since these will rot and cause the rest of your basil to go bad as well. Use those leaves immediately or place them in a plastic bag and store them in the freezer for future use.
Dump and replace the water every few days, to keep it fresh. If the basil was not too dry, it will actually begin to grow and can be transferred to a pot filled with soil or a hydroponic system where it will keep growing. You can snip off leaves as you need them from the ongoing supply.