With the change for DA's effect on most skills, 1st priority is on CnS as always.
For AoE pulls, ideally you just want to start using Abyssal Drain until OOM then recover via Syphon Strike in Grit but using Unleash to let them stick to you is better if you happen to group with impatient healer giving your regen or DPS focusing different targets right at start. Priority on DA is still CnS for this, though it is better to use it for mana if you do huge pulls (6+ above) and Abyssal Drain away. Quietus should be used if you have 3> enemies up, else you should use Bloodspiller. Delirium is normally is normally after you open up with Blood Price on big pulls to keep getting mana while spamming Abyssal Drain. ALWAYS have at least 40-50% mana before you pull next set of mobs to ensure you can hold aggro and keep spamming AoEs.
For single target, just make sure that you don't cap your mana and gauge while still using DA+CnS. Also good if you can recognize if the fight is gonna end very soon that you want to empty out your mana ASAP.
Opener on boss fights: nothing much changes, just the regular PS combo(s) into dropping Grit for more damage, top up aggro accordingly, use Grit as an emergency 'CD' if you will but you lose a GCD which is not ideal. Most people don't consider this but Plunge and CnS still give mana back with Blood Weapon and should ideally be used there. Plunge however has more use in fights where you need to avoid aoes and still want to hit boss the soonest, granted you need to know the exact timing on this. You ideally also want to have full gauge before any boss fights if possible so that you can dump DA+Bloodspiller twice.
The Blackest Night is really great for dungeons and I still hear horror my mates have seen so far when they see DRKs tanking, it's normally better to use the CD early if you are doing huge pulling due to how often it can be up. I usually pull at least 2 sets of mobs (5-8) and still surviving due to Blackest Night. Just now I ran a DREX with solo queue and this healer still did 1.1k DPS (screenshot attached) while I was using 4 i270 slayings. The dragoon's number was pretty low that I even outdpsed him as a tank in dungeon which shouldn't happen normally, else would have been a much shorter DREX. Granted this is done in a JP datacenter, so in NA/EU you would have better luck if you go with people you know.
EDIT: the necro is real btw