I'm a fan of first removing a rubber band at the bottom if there is one. Working with one bundle of herbs at a time, I lay out a couple of sheets of DRY paper towels. Then I pick through the bundle of herbs I'm working with (mostly referring to parsley, chives, dill, cilantro, even scallions) to discard any which look obviously bad or on their way to bad. The bundle gets rolled within the dry paper towels; that roll then goes into a plastic bag and into the refrigerator, where I store the bags in a shelf on the door (which I think is the warmest place in the fridge). Different plastic bag for each herb. As I use the herbs, I may replace the paper towels if they get too damp/moist. I can get some herbs (parsley/dill) to last almost 2 weeks this way. Cilantro and chives about a week (though I haven't used Jacques' tip of freezing cilantro stems to use in cooking - it sounds like a good one). Heartier herbs with woodier stems last longer (thyme, rosemary).
I actually do the same with lettuces after I've rinsed and spun them dry, though I use clean kitchen towels to wrap and enclose. They stay crisp and nice for up to a week this way.
In this fridge, sometimes the crisper drawers get too cold and I've seen lettuce and other soft greens/herbs get a little frostbitten, so I really try to keep them in the door or on a top shelf. My fridge is not for the meek at heart.
