If the herbs come in a sealed plastic package, it's actually a special plastic that lets ethylene gas escape and doesn't let oxygen in, so they will keep for a surprisingly long time if you re-seal the bag after every use.
If you've bought them in bulk, treat them like you would fresh flowers. Prepare a mason jar with a few inches of cold water, cut a half-inch or so off the stem ends of the herbs under running water, then immediately put them in the jar and cover the tops loosely with a plastic bag (don't seal it), and put the whole thing in the refrigerator. Most herbs will keep at least a month this way, often six weeks, especially if you're good about changing the water and pulling out any sprigs that do start to go bad.
That said, I often have some losses if it's something I don't use all the time...



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For instance, yesterday I bought a ginger root the size of my whole hand. It's the average amount of ginger root we buy each time.
Particularly cilantro since I almost always reduce the quantities I use in recipes.