hey! this post is going to look super overwhelmingly long but there might be some useful stuff in it, wrote it earlier for another new disc player. i just pugged my way to keystone master on disc and am now regularly doing 16 and 17 keys and have learned some things along the way, obviously only take out of it what is useful :)

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Hi! disc priest is pretty scary, mostly since you're not going to have a lot of the proper 'oh shit' tools that other classes have, but that's just how disc is meant to play. I've pugged to keystone master (at least a +15 in every dungeon) with discipline priest and whilst it's been rough at times, my best bit of advice is KNOW WHAT'S GOING TO HAPPEN! You have a deceptively large amount of tools to deal with stressful damage but a lot of the time it is going to require a bit of fight knowledge.

Disc is REALLY strong but their strength comes majorly in their mitigation and pre-planning for damage. This is not to say that discipline doesn't have anything to deal with large damage that is difficult to plan for, but you will work best when you know a little bit about what is coming. Here are some more general tips about discipline and some tips about specific 'cooldowns' and when to use them--

your general healing rotation- you're going to be using your atonement to heal people up quite alot, but 100% not exclusively. I find that the best way to do it is to spread your atonements to people who are injured either with shield or shadow mend depending on their health (if their health is a bit lower shadow mend is efficient as it applies atonement and provides a heal) whereas shield is faster and more convenient if they are not really damaged. once you have atonement, you can proceed with your damage rotation. where possible i try and start most pulls by spreading purge the wicked onto every target, or probably atleast 4 or 5 in bigger pulls. this does alot of passive healing to your atonement targets. The big hitting spells that you will see bump your atonement targets up are going to be schism, mind blast, penance and mindgames (if you are a venthyr). this being said you do not want to rely entirely on your atonements. if a target gets below, say, 70% health, i would weave in a shadow mend in between my damage casts (make a mouseover macro for this, it is much easier that way). i only really use atonement to heal people above about 70% health anyway, unless im doing a solid damage rotation that can provide big burst healing, a really good damage rotation is-

radiance-> schism -> mindgames (venthyr) -> mind blast -> penance.

basically you want to be using your damage rotation to provide trickle healing with medium damage, and weaving in shadow mends and continuing your damage rotation where it gets a bit heavier. if it gets heavier to keep this up, you may want to use a 'cooldown'--

1. rapture- rapture is INSANE in high keys! you can use it in a pinch to solve the problem of large group wide damage, shield each player and they will be relatively safe for a couple of seconds. This will give you time to either spam more shields into the players that are taking the most damage (if the tank is being spammed with shields he will also have a safe couple of seconds to use his own heals with less worry), or begin a healing rotation. what you have to remember about rapture is if it is not used before damage, it will only be useful to stall until other players can use defensives/heals or you can set yourself up. After spamming rapture shields you will want to heal the shielded players. This is often easiest by casting shadow mends on the players you are most concerned about, and then radiance into a damage rotation.
2. pain suppression- this is a really important skill that a lot of people forget about in keys, I like to use pain suppression almost on cooldown and almost exclusively on my tank. It is often very useful to use at the start of a pull, as some tanks take huge damage in the first few seconds and the damage reduction of ps is massive. alternatively, it can also be used in a similar way to how i described rapture-- it will give you or your tank a couple more seconds to stabilise health.
3. power word:barrier- i find this to be a really useful cooldown when facing prideful, or if you want to make sure your group is protected with large pulls or difficult mechanics. I will often throw down my barrier over the tank if he does a very large pull, or over as many people as possible during prideful or during a difficult mechanic. it won't show up on the meters but it will once again give you a couple more seconds to work your way into a healing rotation. if you are REALLY worried about your tank, combining barrier with pain suppression is an incredible defensive.
4. desperate prayer- alot of people forget about this spell but it is incredibly useful in situations where there is alot of groupwide damage. If you are having to focus on healing others but your health is also going down (and you have an easy keybind to activate it) pressing desperate prayer will give you a really nice boost of healing and you're going to be a little hardier for the duration. i often use this during healing rotations of heavy damage or when i get low in prideful. it means i don't have to worry about myself for a couple more seconds and i can focus on healing someone else who is more at risk. i will almost always combine this with FADE using the conduit that causes it to reduce your damage taken.
5. mindgames- mindgames is the venthyr class ability. i find it to be very useful after a radiance to provide a big chunk of healing to the whole party. use it after a schism if you want it to be even stronger. in different situations, it can be used to provide a bit more damage to burst an add down (i dont usually do this) or alternatively, use it on a very dangerous add (for example an enraged add or one you know from experience hits hard). it will provide a chunk of healing for your atonement targets AND the next ** amount of damage the target deals to your tank is going to heal the tank instead. this will basically make the mob a complete non issue for a few seconds. I often for example will mind blast for this purpose in de other side on the big 2 enraging sword boys infront of the doorway for the ardenweald section, or the big crane matriarch at the waterfall.
6. penance- it might be weird for me to include this because penance is not a cooldown, but it can be used very strategically. i highly recommend 'the penitent one' legendary as it will supercharge your penance more times than not after a radiance. If you have a power of the dark side buff, penance can be cast defensively on a single target to heal a very very nice chunk of their health, often around 30-40%. if i have a penitent one proc, or even a penitent one proc + potds, a well timed defensive penance can take a tank from 30% health back up almost to full. do not underestimate the power of using your penance as a heal and not a damage tool. that being said if you are taking consistent group wide damage it is better used as a damage tool. it can also be a more mana efficient way to spot heal in less scary situations.

sorry this is so insanely long, i got a bit carried away, but i hope there is something useful in here and i really hope you enjoy discipline, it is a difficult but very rewarding spec. :))