I agree with the general thread so far , especially the idea that its the Knowledge thats important, after all what use is any FAK if nobody knows how to use it.
I was trained in the Forces as an auxilliary medic. The three things stressed to Us the most were B.B.S., or Breathing, Bleeding and Shock
BREATHING; Make sure, as soon as possable that the Victim ( sorry, Casualty) has clear and unobstructed airways, the toungue for instance can fall back and block the throat, though if He's yelling or bitching about how much it 'urts, I think You could take it that the airway is clear.
BLEEDING;Can often look worse than it actually is. The best way to stop it is Direct Pressure ie: press it tightly until it stops. then apply a dressing, and,if possabl a covering of some sorts, Gaffa Tape is quite good for this
SHOCK; Not a lot You can do about this except minimise its effects Its a natural reaction to being damaged. We were taught to keep the casualty as warm as possable, preferably off the cold, damp ground ( Difficult in a cave I know),and to keep them as calm, as You can. One of the most important things was to address the Mental aspect of shock. Try to reassure them . You know the sort of thing, " dont worry, It'll all be alright, You're not that bad , rescue's on its way, I know what I'm Doing, Daves been doing Your Wife whilst You're on Night's". ( Actually, forget the last one), But seriously a posative Mental Attitude can go a long way to minimising the effects.
Now the disclaimer, This is no way a comprehensive guide to First Aid, above OR below ground, I admit that I'm a little Rusty, its been Years since I've had to do this for real, and Techniques and Practices may have changed drasticly.I would recomend that individuals take relevant training for themselves, or at least read up on the subject.
I hope this basic advice is of use.