For starters, pack what you'd put in a backpacking kit, but more of it. More bandages, including large ones capable of sopping up lots of blood, plus elastic bandages, gauze pads, adhesive tape, a wide range of stick-on bandages (brand-name Band-Aids, for instance); over-the-counter painkillers such as aspirin, ibuprofen, and acetaminophen; over-the-counter remedies for diarrhea and colds/flu; an antiseptic such as Betadine; and antibiotic/cortisone creams to treat minor cuts and skin rashes. Plus tools such as forceps, scissors, tweezers, and scalpels. And masks and gloves for protection against infectious agents.
You can make life easier simply by purchasing a ready-made kit such as those made by Adventure Medical Kits (www.adventuremedicalkits.com). Their expedition pack goes for $240 and is designed to cover a big group for up to three or four weeks. It includes extremely useful pocket guides for treating common injuries.
After you purchase that, it's time to see a physician who is familiar with mountaineering. That's because you'll need some prescription medications. Specifically, several broad-spectrum antibiotics, some moderately powerful painkillers, and perhaps some drugs that treat high-altitude sickness, such as Diamox (which helps prevent high-altitude pulmonary and cerebral edemas) and Dexamethasone (a steroid to reduce brain swelling).
Of course, you're also going to need to know how to use all this stuff. So a good first-aid course is very much in order, preferably one that deals with expedition and mountaineering issues. Check for courses run by the National Outdoor Leadership School (www.nols.edu) or Outward Bound (www.outwardbound.org); also look for listings at your local climbing club.
Finally, you'll need the most important thing of all: The willingness to apply what you know. That seems to be the biggest hurdle in accident situations. You have people standing around who might know what to do, but they're afraid of making the wrong decision. But lives may depend on making a decision, so you've got to have the confidence to wade in.