There are several different ways to store fresh basil. We've read about placing cut basil in a plastic bag with damp paper towels and stashing it in the fridge. We're heard about chopping the leaves into bits and putting them in ice cube trays, then freezing for later use. But our personal favorite is this:
Snip off the ends of the stems, as you would fresh flowers
Fill a jar or glass with cool water and push in stems
Fit a plastic bag loosely over basil
Store on counter at room temperature. (Storing in the refrigerator can turn leaves brown more quickly.)
That's it. With this storage method, your fresh basil should be good for 1 to 2 weeks.