The way healing is set up in ffxiv you can play your class in a very versatile manner. As someone who is primarily a sch and have smn and brd as secondary jobs I would like to share a few tips.
1: Heal, its what your there for. Arrange your party list to suit your healing styles. Myself I click on the pt list so I group up tanks/healers/dps cause that is easiest for me. Find what's easiest for you and go for it.
2: Don't be afraid to ask for ballad and don't wait til your completely or nearly out of MP. Shroud of saints is nice for whm and sch has Aetherflow+Energy Drain. If there is no bard in the pt, whm needs to manage mp much more carefully than sch so utilize your free cures and stop spamming Cure II unless you need to. Regardless, don't rely on your bard to watch your MP. Make a "Ballad please!" macro to make things faster and easier. Blaming the brd for not watching your mp is usually just bad form.
3: SE gave both whm and sch multiple ways to help dps and nothing is more irritating when I am on a dps job than a healer who sits on their hands and does nothing if there is no need to heal. I will refuse to sleep mobs if your not going to do anything. DPS shouldn't be your main concern but doing absolutely nothing is a fail healer and typically will get you a boot if you are in one of our group pts. There is no reason not to dps if there is nothing else for you to do. When I am on sch I will dps as much as I can when there is no healing to be done and everyone appreciates it.
4: Watch your agro! There are small bars under your job icon that shows your agro level as well as colored icons next to the mob names. If you are pulling hate to easy, generally that means to slow down. For instance, don't spam curaga II in titan, even good tanks have a hard time holding agro if you curaga II spam. Usually a single Curaga is sufficient if there are two healers and this splits the enmity generated.
5: This one is for sch. Don't forget at 50 you get this handy dandy ability called Lustrate which restores a good chunk of hp to the target. You need Aetherflow to use it and it is a giant mp saver and can prevent wipes if used correctly. Have this ability in an easy to access slot since its good to use in emergency situations. Also utilize sacred soil when needed. I use this often in fights like primals when they do their big aoes. It saves mp and helps keep some players up.
6: Another one for sch. There are many times your pet will be useless at your side so don't forget to "place" your fairy in the appropriate spots. This can be done starting at 30 when you unlock sch. Place Eos near your tank or Selene near the pt members that will best use her buffs. You can move them around as well, once you practice a little you will be able to place and replace your fairies with minimal effort. Having Eos near your tank in some dungeons will provide enough healing for you to dps most the dungeon through, speeding up the kills and making things flow smoother.
7: I cannot stress this more!!! When you get hate, DONT RUN AWAY!!! Take the mob to the tank or stand still to allow the dps to take it off you. Only run away as a last resort! Running away from the pt, particularly the tank will get you killed and rightfully so. If you are running away from the ppl who can take the mob off you, you are a detriment to the pt and are just making things needlessly more difficult.
8: Stay in back, there is no reason for you to run head first into a group of mobs, that's what the tank is for.
9: Watch your surroundings. Sure you are watching hp bars, mp bars and so on but you also need to make sure you are in the clear so you don't accidently agro mobs in another room or that may sneak up behind you. Usually this isn't an issue but its good to keep in mind.
10: Know when not to use regen. When pulling a group of mobs there is seldom a need for regen as it will just get you enmity and cause the mobs to turn tail and come after you. If your tank is going to do a large pull, applying stoneskin prior to the tank pulling the first mob is your better choice. For sch a combo of stoneskin+adloquium is your go to.
That's all I can think of off the top of my head. Hopefully a few of these tips help and if you have more, please feel free to add some suggestions below!