1)Use the right spells
This means selecting the right heal for the job. 80% of your heals at least should be your mana efficient spell. If your tank is ever not at full life you shouldn’t be just standing there, you should be casting your mana efficient spell on him. If you have a mana regen ability for 20% of your mana, cast it at 80%. There is a good chance it will be back up by the end of the fight. Know what’s an effective group heal is for your class, for resto druids it’s popping into tree of life and spamming life bloom on everyone or tranquility. You may want to even spec into the quicker tranquility cast if you are having a hard time.
I have seen several healers complain about mana and then not take an ability that saves them like 6% mana. Right now you should be taking every single ability that lessens the cost of spells or gives mana back. You should be avoiding buffing abilities that cost lots of mana. What good is an awesome regrowth if I cast it twice a run?
Avoid haste if you have mana problems. I know it was awesome in wrath, but it's not anymore. Haste increases your healing per second at the exact rate it increases your mana cost per second. In other words it doesn’t help mana efficiency, while mastery and crit do. Learn which is better for your class. crit or mastery – it’s not always mastery disc priest and resto druids.
3)Know what other classes can do and make them do it:
For example: The rogue ability recuperate is awesome, make them use it. Pally’s get lay of hands, every 10 minutes they can fill someone’s life up all the way. Make them use it. Lots of classes get some abilities to avoid damage: barkskin, cloak of shadow, etc. Make them us it.
A large part of tanking at this point is using your cool downs properly. Every tank gets 3 or 4 cool downs to help them avoid damage. Typically they have one short cool down (30secondsish) and longer ones (once per fight). Coordinate with them!
4) Work with DPS
Know the fights and tell people what to do, a lot of damage can be avoided all together. Interrupts/CC are your bff’s. Don’t be afraid to intentionally let a DPS die if they are doing something wrong. It sends a message and if they get their stuff together everyone will be happier. I’ve notice a ton of people taking damage from completely avoidable abilities because they don’t know how to avoid it.
Also, the better your DPSers are in terms of DPS the quicker the fights over. If a fight ends in 3 minutes instead of 4 minutes you have to do 25% less healing.