how to store shiso leaves?

I've had reasonable luck just keeping them in the refrigerator, but if you want to keep them longer, one traditional way is to salt them. Sprinkle some salt between each layer and keep them in a non0reactive container in the refrigerator. As you might guess, they'll exude some water and turn a darker color. But they remain tasty. Rinse or not, depending on the taste you're going for.

Another option is to freeze them. Like with the salting method, they turn dark and the texture changes but you can still use them.