I will probably be using a LOT of screenshots in this thread. Consider yourself warned!
The Number 1 Rule Of Partying
STICK TOGETHER! A party can and usually will dive much further than any of the members could by themselves. This is only effective as long as the party functions as one unit: all members must contribute their melee damage, their healing, and their firepower to the same fight. In this way, it's as if one über-powerful character is walking around slaughtering the monsters!

OK, the scene shown above might be a bit overkill. However, the idea is this: the monsters are designed to challenge a SOLITARY player who has levels and gear appropriate to that depth. So if you have two or three players fighting that monster at once, the advantage is so much greater that you can do it with gimp gear and low levels (the whole point of powerdiving in parties). So why do low level parties get wiped so often? The biggest reason is that they do not stay close together! A mix of character classes and MAngband ability often results in differing play styles, and so the natural tendency is to split apart. Some players might run ahead because they don't want to wait for casters to rest, or because they hunger for battle. Impatience is a big killer, because not all classes are equal at the same level (and so the weaker classes advance the slowest). In addition, since EXP is gained somewhat slowly in parties, it's not uncommon for some players to go chase after every monster they can find to get some extra EXP. Finally, some players don't change their play style in party situations and just go on as if they were solo. This is the worst, because (1) other party members might have been counting on your support, and (2) it's no different than diving by yourself at depths you would normally avoid, and with gimp gear. This is just asking for death! Whenever someone separates themselves from the group, they are bound to get in trouble:

What if someone lags behind? Don't "wait for them to catch up". Turn right around and get back to them. It doesn't matter if there are several more @'s running ahead and only one lagging behind; you should run back and stick with the one who fell behind, even if the others don't stop. Whoever gets separated from the group is more likely to die, so never leave anyone alone for too long. Remember, they can't see the same corridors that you have explored, so they are likely to take a wrong path while trying to catch up to you and thus get separated even further.
I think you should always keep an eye on your formation when you are in large groups. If you notice the group split apart, don't hesitate to point it out. It's not rude to request that the party regroup if too many @'s have gone their separate ways. What's rude is running ahead and not waiting for everyone else.
Yes, most of this is pretty obvious, but you'd be surprised how many people ignore this most basic rule.
Party Size, Class Distribution, and Formation
What's the optimum group size? It really depends on what classes are in the party. For a mixed class group, 3-4 is best. For a group consisting of melee-only classes, 2 is best. Actually, any group should not have more than 2 "tanks", because boredom will set in very quickly and the tanks will wind up going their separate ways looking for something to fight. Similarly, groups larger than 4 become somewhat unwieldy. Pits and vaults specifically are hard to tackle with a huge group. It's also a lot easier for the @'s to split apart when there are a lot of them running around.

The best way to deal with a huge party is to split it into subgroups that stay on separate dungeon levels. Smaller groups are generally more efficient, and of course the exp is better.
Now what classes should go in each group? If one group has a Mage, it will need at least one tank; fortunately, almost any class can tank for a mage. If there is a Priest, they will want a somewhat stronger melee class to tank, such as a Paladin or Warrior. This way, the priest can focus on healing. Aim for a balance between front and back line classes: too many tanks, and the party will break up; too many squishies, and the party will be easy to kill if it gets mobbed.

The above formation is pretty good: two tanks and two support classes. With lots of open space like that, the group formation is rather flexible. However, in tight spaces, positioning of the @'s is a lot more important. The reason is that archers and casters can shoot through other players, but healers can not. Thus it is very important that healers have line of sight to the tanks at all times! In narrow corridors, this means that the priest should stand directly behind the tank. Also, when fighting a huge mob such as an Orc unique, the tank shouldn't run straight inside where he is likely to be surrounded, because this will block LOS for healing.

Pooling Cash and Gear
This is a vital strategy for level 1 dives. The basic idea is "don't be greedy". Equipment decisions should be made based on what benefits the party as a whole. When you find ego items, try to give them to whichever party member will benefit the most. Don't be greedy: either more ego items will show up later and you'll have your chance at them, or the whole party will die and nobody will keep anything. Heavy armour and high damage weapons should go to the tank, items that boost stats should go to characters who depend the most on that stat (WIS for priest caste, INT for mage caste, etc.), books should go to the players who can cast from them, light armor for mages, blunt weapons for priests, wands and rods for back line classes, and so on.
Pooling gold is generally a good idea as well. Since carrying capacity is based mainly on STR, weaker players will often leave the heavier (and often more valuable) gear to be carried by the strong players. Once the party has returned to town, those with high CHR should sell the group's loot. The gold pool can then be used to buy what the group as a whole needs the most; this could be a single "big-ticket" item such as more damage for the tank or a stat-boosting item for the caster.
Phew! That was a hefty post... I'll take a break for now, expect some more later.