If you buy packs of fresh herbs from your supermarket, take them out of the packaging and soak them in ice-cold water for about 1/2 hour (but don’t do this with basil). Then drain well, wrap them loosely in kitchen paper and put in a poly bag, allowing some air to slightly fill the bag, or put them in a plastic box.
Store in the fridge. Most herbs will keep for a week like this. With basil, just rinse briefly, as it is so delicate.
Check herbs occasionally and discard any browning or slimy leaves.
If growing herbs in pots, put them on a window-sill in good light, water occasionally and harvest regularly.
Another way is to put the stems in water in a big cup and cover with a ziplock bag, not tight. All you have to do is take the cup out and cut what you need. Change the water about every 3 days.. It keeps over a week this way… You can do cilantro, parsley, asparagus, etc this way.