EDIT: Did a major update since this got way more attention than I expected. This is a Guide for using Ancient Teachings of the Monastery legendary (ATOTM).
Talents:
Mistwrap
Lifecycles
Invoke Chi-ji, the Red Crane
Rising Mist
So to talk a little about the talent choices here, mist wrap is pretty standard for M+ content. The big change here is that I recommend Lifecycles over Mana Tea, which is contrary to the vast majority of monk guides. The reason why is that you can benefit from it on nearly every single vivify/enveloping mist cast if you do it right, and it ends up being much more mana saved than mana tea and it’s much easier to use.
Covenant:
Overall, the covenant doesn’t really matter all that much. You can play whichever is most fun for you or play whichever will get you into the group faster (usually the dungeon covenant). None of the covenants directly buff ATOTM by some considerable amount.
Kyrian - Weapons of Order resets your Essence font and grants a ton of mastery. The essence font reset is okay/fun but in high hps scenarios you really are just popping WoO for the huge mastery buff it gives you.
Necrolord - Bone Dust Brew makes it so you can simultaneously do a little burst window of damage and healing. You will want to have Thunder focus tea as well as 3x stacks of Teachings of the Monastery before using it so you can fit in double RSK as well as BoK fish for reset. From my experiences, it’s not very good for healing but is better used for just doing damage. You can also use it on a big AoE pull and spam SCK.
Nightfae - I haven’t played night Fae so I don’t have much to say here. I will update it when I do play it some. It has a high mana cost and short range so it mostly useful for dealing damage when you can spare the mana.
Stat Priority:
Mastery up to 100%, haste to at least 10% and then the rest in crit/vers.
Mastery is a very very strong throughput healing stat. You can stack more than 100% if you are struggling with keeping people alive, but at around 100% is a sweet spot where you can do the majority of low HPs Healing with just ATOTM and using renewing mist to trigger gusts of mist on injured targets without having to cast vivify. Also, having it at around 100% makes Chi-ji a potent cool down too since it scales with mastery.
On certain affixes you may want to use more than 100% mastery (grievous fortified says hello, or fort bursting weeks) because it really does make a huge difference in throughput. If you are playing a crit/vers build you will have to burn so much more mana to keep people alive than with mastery. You lose out on some* dps though (but realize that the amount you lose on is marginal there is a lot of discussion below about dps but it’s seriously a tiny amount that is way over exaggerated by certain people in the thread; the throughput increase is much much much more significant and valuable than the tiny dps loss).
Rotation:
The primary goal is to maintain 100% uptime on Essence Font on the party by extending the HoT effect with Rising Sun Kick, but not to cast Essence Font until ATOTM buff is about to fall off. (There is about a 5 second window where EF is available but you still have ATOTM and you want to avoid pressing EF early because it’s just going to drain your mana over time).
When stacking mastery, the rotation changes slightly, with the primary change being how you use Renewing Mist.
In traditional fistweaving guides, it is reccomended that you use Renewing Mist on cooldown in order to extend their durations and have as many active as possible for vivify cleave.
But when your mastery is at 100% or higher, its better to just hold onto Renewing Mists until damage goes out. This way you can trigger gusts of mist on injured targets, and because of Essence Font and the Resplendent Mist conduit, it heals for a lot and you can keep DPSing without casting vivify.
Opener- Typical opener looks like: Enveloping Mist on the tank and then channel essence font. This makes it so the full channel of essence font is magnified on the tank from mist wrap. Then, cast renewing mist on the tank as you get in melee range so you can immediately Thunder focus tea rising sun kick.
Now you have two choices for ATOTM:
1)Alternate Tiger Palm and Black out Kick (results in the most RSK resets and Is a steady stream of healing)
2)Build up Tiger Palm to 3x and Black Out Kick
(Results in the most burst healing)
I think it’s best to alternate dynamically between the two. As you get experience with the play style you will know when to stop alternating and start to build up to 3x stacks. Examples include whenever predictable damage is going out like Soggodon’s seismic wave, or when the tank is going to get hit by a tank buster. You will learn to line up your 3x stack and/or delay your RSK or black out kick dump for immediately after these events to benefit the most from ATOTM healing.
One of easiest and most effective ways to improve your mana efficiency as a monk is to never cast Enveloping mist unless you have a Rising Sun Kick available. Never cast 2 or more EVMs unless you have 2 RSKs available or a RSK and 3 blackout kicks banked up.
With high mastery, the supplemental healing from Gust of Mists by casting Renewing Mists is sufficient to maintain an ATOTM healing profile much longer. Since GoM heals for so much, you do not have to cast anywhere near the number of vivify or enveloping mists that other monks will have to cast, allowing you to have more uptime DPSing. Even when you do have to hard cast Vivify or EVM, their power is magnified by a ton.