(Disclaimer: as I said above, withered army training doesn't yield anything terribly important. It's a source of up to 500 Nightfallen rep every couple of days, and a toy and a pet. You can get the rep in other ways.)
The guide I posted at the top of this thread has a section on withered army training. This map
is also useful, as is this video guide
Guides will tell you to get as far as you can and then go back and pick up chests. This is bad advice at the beginning, because you don't know how far you can get without losing your army, and if you lose your army you can't pick up any chests. You instead want to target specific upgrades on your early runs. Referencing the reddit map:
* Blue upgrades only cost five withered, and are the best except when they aren't upgrades (like the bank item or the toy).
* The +25% damage upgrade is the most important, but to get to it you'll have to fight Dro (the swordsman), possibly losing all but one of your army, and navigate past the Elfbreaker (the ettin), who will murder your army if you don't have 20ish withered or a lot of stuns (which as a DH you do not). If you can get back up to 5 withered after fighting Dro, you can wait for the ettin to path away and sneak over to the chest as your final act.
* The anti-fear and health upgrades can be obtained without fighting Dro, and are pretty useful.
I've been doing this as a tank and spending 2000 ancient mana each run, which is the easiest option. I miserably failed my first couple of runs, spent the next few runs targeting chests, and was finally able to clear the whole area on my last run except for the room which requires two berkerkers to open. That'll be my target in the next run, to pick up the Box of Calming Whispers. Once you pick up all of the boxes, you can just focus on getting to 400 points, which at that point will be easy.
Spec for any stuns or disorients you can; for a vengeance DH this means Fel Eruption and (less important) Quickened Sigils. You want them for the elementals to stop their explosions until you have to brute force to murder them before they explode. You want them for Dro to stop him from charging around, and for Elfbreaker to stop his stomps. Stuns will not be enough if you don't have the DPS to kill enemies before they repeat their mechanics, so it's hard to make a lot of additional progress if you lose all but one of your army to Dro.