Healing and WHM specific breakdown

Healing
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Basic skills
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Stutter stepping: As a caster (especially a white mage) your movement is limited. Virtually all of your gcds are full length cast times, so unless you need to pop a regen on a tank or reapply your dot to the boss, you're rooted in place, or so it would seem. While casting, there is about a half second window at the end of the cast where you can move without interrupting your cast. Mastering this small movement can allow you to reposition without dropping a gcd or using a weaker move that has a shorter cast time. This being said, there will be times when you need to move a large distance immediately. Always try to fill this time with SOME sort of gcd, healing or dps, via use of lily moves, regen, dot reapplication (dont do this unless your dot is like 3 or fewer seconds from expiring), or swiftcast.

Always Be Casting: If you ever find yourself doing nothing, hit tab immediately and start casting glare on the boss. Even if you should have cast a heal on someone and they end up dying, doing something is always better than doing nothing. This will also get you comfortable with how a fight flows and tries to mess with your casts (because you have to move, for example). Defaulting to dpsing is a large part of how i learn how many casts i can get off during mechanics, where i absolutely need to heal instead of dps, etc. The reason i encourage dpsing over just slamming cure 2s on your tank is 1) its cheaper on mp and 2) if you intentionally overheal a lot with the thought "I just wont later" you'll have to reprog that section because you dont know how much of your healing was required.

Target Swapping: Obviously, in order to cast a heal you need to change your target from the boss to who needs hp. You can swap targets in this game while casting something, and the cast will land on whatever you were targeting when you were casting. When I'm healing i am constantly hovering my mouse near my party list, clicking on potential heal targets, and then hitting tab to go back to the boss as soon as my heal cast has started. While this doesnt work for targeted ogcds, its how the vast majority of my healing operates. If you dont like this much hand movement (I personally use it to keep myself active and focused) you can use mouseover macros. Ask someone else about those because I have never touched them (weables and wawl i know have experience with them)

Communication: Healing is a two person job, and playing even remotely well requires knowing what your partner is going to do. If both of you dump big cooldowns on the same shit, you wont have anything for upcoming problems. Talking to your cohealer to figure out what they're doing and how you can play around each other's kit is essential. The same goes for talking to the team about mitigation. You can almost assuredly sneak past the first two maybe even three fights without talking much, except maybe on a few key mechanics, but that will fall apart eventually (think e4s phase 3) and its best to learn how to optimize as early as possible.

I would also recommend learning about how much all of your moves heal for (non-crits since you cant predict those) in order to better understand what damage values mean in terms of how much healing you will need to do. Just dry fire moves in town a lot until you have a rough idea of how much stuff heals for.

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White Mage Toolkit
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White Mage is arguably interesting in that it has very few ogcd heals, but very strong gcd heals. There may be quite a few cases where your best course of action after raid damage is to do nothing, and let your cohealer take care of it. Maybe you'll just throw a medica 2 at the situation and call it a day. In any case, Below is my personal breakdown of every white mage spell and what its good for, when to use it, and just general notes.

GCD Spells:
Glare - 300 potency, its what you do for 80+% of the fight
Dia - 120 potency instant cast with a 600 potency dot over 30 seconds for a total of 720, you keep this on the boss at all times,
         ideally refreshing right as it expires
Holy - 140 potency aoe, optimal on 3+ targets (would be 420 potency per cast on 3), I bring this up cuz it looks like we might get a 2
         bosses at the same time fight this tier. As whm, you DO NOT cast your aoe spell on 2 targets.
Cure - 400 potency, 1 ogcd slot generated. Dont use this unless you really really have to (very low mp being about the only excuse)
Cure 2 - 700 potency, if someone needs hp immediately and you have no lilies or ogcds, this is what you press
Cure 3 - 550 potency aoe, tiny radius, if you ever plan on casting this, you MUST tell the group when so they can stack up. It costs a
         lot, but in tandem with thin air its just a busted aoe heal.
Medica - 300 potency aoe, big radius, standard fare aoe heal, should be used as little as possible
Medica 2 - 200 potency aoe with 500 potency regen over 15 seconds, largest heal radius in the game. If you gcd aoe heal, you should
         virtually always be using this first. Let the regen bring people to full (mechanics allowing)
Regen - instant cast 1800 potency regen over 18 seconds, the gold standard in bang for your buck, this is your most powerful heal
         outside of bene. Will almost exclusively be used on tanks. Can start pulls by casting on the MT 5 seconds before pull
Esuna - Removes a debuff from the target. Not likely to be relevant, if it is and theres only one debuff, make the bard do it

Thats it for your standard gcd stuff, lets talk lilies.
So you start a fight with 0 lilies, and you generate 1 every 30 seconds. Each one of these can be used on one of two healing spells, and once you have spent three in this fashion you can use the dps spell for free (it does not cost a lily.)

So, here are the lily spells available to you:
Afflatus Solace - 700 potency instant cast, its cure 2 but instant, costs no mp, and generates 1/3 of the dps spell. Basically, use
         this if you are planning on using cure 2, have to move far and your tank already has a regen on them, or need a panic heal
Afflatus Rapture - 300 potency instant aoe, its medica 1 but instant, costs no mp, and generates 1/3 of the dps spell. Use this in the
         same situation as above, but replace the word cure 2 with medica.
Afflatus Misery - 900 potency instant cast aoe damage with slight falloff per target, can only be cast after 3 healing lily spells.
         There is no downside to using this, you get to move for free, two ogcd slots, no mp cost. That being said, save it for when
         you need to move or weave ogcds, because it does not expire. The exception to this is if you plan on using another lily spell
         before either of those things happen.

So the tldr here: lily spells are tools for weaving and moving, and they are the most efficient healing gcds in terms of DPS. since you get a 900 potency dps spell for casting three of them, you only lose 1 glare per 3 healing gcds cast (the math goes you lose a glare per each heal spell, and then a fourth is replaced by the lily dps spell, so you get 900 potency but lose 1200). In general, its fine to sit on 3 stacks of the healing lilies, only use them when you need them. If a boss goes away, you can dump however many you feel comfortable with in order to get a Misery cast without losing gcds while the boss is targetable, which is a decent dps gain. If there is more than 1 target, Misery is a dps gain, and you should build to it intentionally even if the boss(es) dont go away.

Alright with gcds aside, ogcds are all thats left:
Tetragrammaton - 700 pot, 60s cd, you throw this at a tank once their hp goes to about half, should pretty much never be off cd unless
                 you need to save it for a very specific heal on someone
Benediction - Heal target to full, 3 min cd, useful when you have a non pld invuln going off. That said, its cd is short, so you could
                 probably find a spot to just throw it at a tank taking autos in most fights between invulns.
Lucid Dreaming - mana refresh (potency here means nothing really, but its 350), 60s cd, keep this on cd at all times or you will bleed
                 mp. I generally pop it for the first time after like 10-20 seconds of a fight starting DO NOT WAIT FOR YOUR MP TO BE
                 LOW TO PRESS THIS
Asylum - 800 potency regen bubble over 24 seconds, buffs healing received by those inside by 10%, 90s cd, very good for cases of
                 sustained damage, or to top off the party when no more damage will come out for a while. Requires loose stacking
Assize - 400 potency aoe heal AND damage, restores 500 mp, 45s cd, basically use on cooldown, can hold for a few seconds if some
                 raidwide damage is happening shortly after it comes up, but never hold for more than like 10 seconds imo
Presence of Mind - 20% haste for 15 seconds, 2 and a half min cd, use this in your opener (weave it after dia probably) and keep it on
                 cd, its a really weird thing to have but it just lets you get more gcds out during a fight.
Thin Air - Spells cost 0 for 12 seconds, 2 min cd, use this when you A) are casting a lot of gcd heals (especially cure 3) or B) have
                 to rez. DO NOT WAIT FOR YOUR MP TO BE LOW TO PRESS THIS
Divine Benison - 500 potency shield on target, 30s cd, keep on cd by throwing on the tank, can use about 10 seconds prepull. This thing
                 is honestly wimpy, but two casts shields more than a cure 2 heals for so its worth pressing.
Plenary Indulgence - 60s cd, grants a buff to nearby players that heals for 200 pot whenever they are hit by any of your aoe heals for
                 10s. Can use this if you just need a bit more healing to not have to cast another gcd, or when using many aoe heals.
                 Think of this as adding 200 pot to your next one or two aoes.
Temperance - 20% healing up, 10% damage taken down for a large radius around you for 20s, 2 min cd. Its a mitigation skill, thats all.
Fluid Aura - A broken shell of a spell :( (its a bind, you dont need this on your bar)

I think thats every spell, hopefully I didnt miss anything. Honestly I think breaking down each spell's use case is a good way to go about figuring out how to heal. Knowing what situations you should be using stuff in is the first step, identifying those situations is the next. I still think the best healing advice I ever received was "Dont be afraid to let people die, you have to optimize your own shit just like everyone else." Obviously, dont be an idiot about things, and play how you're comfortable. If you dont want to squeeze out every last gcd for dps that you can, chances are you dont HAVE to. In alexander ultimate, I threw a huge number of heals for safety because it just wasnt worth losing the prog time if we got high damage rolls or few parries or whatever the hell.