The farmer’s markets are starting to have fresh basil. I have tried many ways to store basil and this is my most successful technique.
Hold a bunch of fresh basil stem side up and snip off ~ 1/4 to 1/2 inch of the stem depending on the length of the stem. Place the basil in a glass of water and leave on the counter top at room temperature.
The basil will last a week or longer and may even grow roots if you don’t use it quickly.