First off I will like to show of two videos, where somebody explains the general premise. I will go into a bit more depth, and explain some of the problems I have solved after.
As you can see in the vids, he runs through from the last waypoint available, from quest III-7(b):
Run through that level and get through the door. This spawn is WRONG:
This spawn is right:
Until you get the right one, leave and resume, and run through the tower again. Once you get the right one, when you leave and resume, you go back to the checkpoint you got when you entered the right zone. This is very important, and greatly speeds up the runs. Getting the checkpoint is the hard part.
You are on a big stairway, the immediate area to the right is one of the platforms where you want to 'drag' elite packs. You run up to them and agro them, then get right up to the edge, and die. You respawn at the top of the stairs. Proceed to dps them down without getting hurt! When they get low, swap out to full MF gear, and finish the job for good loot.
The red lines are for mobs/bad places you are standing, green are for good places to stand.
Here are bad places to stand if they have Teleport(TP), Mortar(MR) or Frozen(FR). They can and will kill you:
Here are much better places to stand, but can still be a bit weird sometimes:
Down the stairs you started on, there is a small bridge, and to the left of it you can see the platform below you. Here is another area to drag elites, using the same method described above. This is a bad place to stand. Small gap, hard to find the right angles to get everything:
This is much better. Easy to drag them to the general area, you can even stand out of the enrage AoE from the right places here. And of course, out of range of TP, MR and FR:
This also works, the mobs often get stuck on the circled areas. You are safe right in the corner there, with good vision as well:
This is very, very bad. Often, when initially checking if any groups have spawned, we will be surprised by 3 teleporting spearmen, who happily jump the gap and ace us. Again, its only TP, FR and MR you have to worry about, but make sure you know the affix before you stand here:
That sums up most of it. You fight your way through all of the random whites (be careful of the ghoul spawns) and find elites, dragging them to the death zones specified. Goblins are really common, probably just under 50% chance of finding one imo. Typically find 2 elite packs, but sometimes 1 and sometimes 4.
If you get a bad pack annoying you on the stairs, just leave/resume to reset. Seriously, its not worth the battle.
Remember, that once you have found the right spawn once, you NEVER have to run through the previous section until you lose the checkpoint by swapping missions. If you leave/resume and you are in town, the game has spawned the wrong instance of the tower. Just leave/resume until you get the right one again, you will respawn on the stairs when its right.
Keep in mind that I'm not preaching 'awesome' drops, simply the best method I have found for dropping the most rares in the shortest time. Act 3, so up to ilevel 63, I run it with 4 people, we get 1-2 rares per pack on average. Roughly 10 rares every ten minutes for the group, and we share pretty everything.
Demon Hunter: I run hungering arrow/devouring, and nether tentacles. SS is a must for reflect damage groups. Bat companion is perfect for spamming more tentacles, for more dps. Other spells are optional, I use caltrops with the slow rune to make the ghouls easier to handle, and to keep any fast packs under control.
Barbarian: Obviously can't dps it himself, but Ignore Pain with the group rune really for reflect damage packs, and helps to clear out the whites with us. Another soldier standing there in MF gear.
Monk: Get the skill that increases party damage, bring your healing spells too. Healing is great for reflects damage.
Witch Doctor: Really not much to say, have never run it with a WD. Splinters I'm guessing, maybe the poison geyser for your spender. I don't think any spawns will be useful over the gap.