As a career SCH, allow me:

Generally a SCH is going to use 3 hotbar sets. One with all your heals and buffs, one with pet commands, and one with damage spells and self-use items like Hi Elixirs and Spine Drops.

SCH is much more versatile as a healer than WHM is (and I like WHM). The name of the game is to use your shieldcures like Adloquium and Succor to cover the party for a second while you put up DoTs on the enemies. During this phase your Fairy can handle any minor heals that go through the shields. Once your DoTs are up, the enemies are taking damage while you go back to healing. Rinse, Repeat.


How a SCH deals with mobs:

Fairy is ALWAYS on Obey > Steady. This lets her cast her heal on her own, but also lets you command her special moves at will.
>Adlo the tank
>Tank pulls and AOEs
>Succor, Rouse
>Shadowflare, Bio II, Bio, Miasma, Bane
>Physic and Adlo tank, top everyone up.
>Reapply DoTs or cast Ruin depending on how many mobs are left. Aetherflow as necessary.
>Repeat.

On bosses is where things get a little rough for SCH. We make murdermeat out of trash mobs, but we only have one "big" cure spell (Lustrate), and we can only use it 3 times per minute. We also don't get it until level 50. Our other abilities are little better than Cure I from WHM. Most boss fights are going to boil down to:

>Adlo the tank and Succor everyone else.
>[Place] Fairy somewhere convenient within reach of everyone.
>Apply DoTs to the boss on the pull, but depending on the team you may not have the chance to reapply them. Remember that you're a healer first.
>If someone other than the tank is taking minor damage (>75%HP remains), let the Fairy handle them unless they actively have hate from something.
>When the tank takes damage, cast Adlo and then Physic. The first heals a bit and then shields them while Physic goes off to heal more as the shield prevents their HP from dropping further. This one-two punch is our equivalent to Cure II.
>For minor AOE damage to the party, cast Succor. and let your Fairy top everyone up. For major AOE damage, precast Sacred Soil (a barrier than totally nullifies 10% of all incoming damage in a fixed AOE) while using Rouse and commanding your Fairy to use Fey Illumination and then Whispering Dawn. Fey grants you and the fairy both a 20% healing power buff. THEN you use Succor and the Fairy uses Whispering Dawn, which is an AOE regen that you just boosted by 60% with Rouse and Fey. That can fill the whole party up from near death in just moment. Pulling off this combo of moves while everyone is in the double digits and not letting anyone die is one of the key tests of a SCHs skill.
>If the tank or someone else is getting sledgehammered and is about to die, use Lustrate. This skill uses up your Aetherflow stacks, but each use recovers 25% of the targets max HP, it is instant, and has virtually no cooldown. You can take the tank from 25% to full in less than one second. Lustrate is also good if you're curingbombing the tank and someone else suddenly takes a big hit. You can use a Lustrate to heal them instantly (and let the Fairy top them off) without having to wait for a GCD to get back on the tank. Same too if someone like a DD is tanking an add and you're dodging AOEs and can't wait for cast time for a regular heal.
>If you're using SCH properly you're going to be burning some MP. Don't be afraid to use Energy Drain, especially on bosses. On HM Garuda I always burn by first stack of Aetherflow on ED after the first phase and all the Succoring/Physicing/DoTing that goes on. That makes sure that I'm at full MP by the time the sisters appear.
>Sometimes Curebombing is the only way to go. Healers naturally hate to do this because it burns tons of MP and generates lots of hate, but there are times when planting yourself in one spot and wearing the finish off your Succor button is the only way to get through a rough spot. Our heal potency is weak, so at the worst of moments you may have to make it up with volume.
>You NEED Swiftcast, which you probably already have. Its for more than Raise though. Swiftcast > Shadowflare is great for trash and Swiftcast > Succor > Succor is powerful for AOEs. If the tank is getting creamed and you're behind on your rotation, Swiftcast > Adlo > Lustrate to get caught up.
>Virus reduces all the boss's stats by 15% for 15 seconds. Use it right before BIG damage or big AOEs. Right before HM Titan Stomps is probably the perfect moment, it can knock almost 80 damage off each Tumult.
>Eye for an Eye is best right at the start of large trash pulls. Like that one hallway in Haukke HM where you get like 6 mobs linking. What E4E does it puts a status on the targeted player, and every enemy that hits him in the next few seconds has a CHANCE to get stuck with a debuff that drops their damage by 10%. The more mobs hitting him at once, the more powerful its effect because more of them can trigger it. Also good for bosses with lots of tanked adds. Drop it on the OT and keep them alive a little longer.
>Try to use Shadow Flare a lot. The damage it does is weak, but it causes a Slow effect on any mobs in the effect area that can prevent a lot of damage. Its active mitigation, and probly my favorite spell.
>If a bunch of adds are on you, use Miasma II. Its am instant, circular AOE around you and causes Heavy, letting you run away from the mobs so the DDs can handle them.

And always remember: "When The Going Gets Tough, The Tough Rouse Their Fairies."