I recently switched my priest to holy and was struggling for the first week or so, here's whats changed recently for me to improve (having no issues healing the new heroics now)
Holy word serenity - heal, these two are your main go to spells during any non heavy damage encounter, always keep HW: S on cooldown, and follow it up with heals if there is only a small hp loss.
Greater heal - when your HW: S and heal cant outheal the damage incomming this works wonders to top off again, once again standard damage speed )just bigger hits)
Aoe damage you wanna switch to sanctuary, keep POH and COH going to top everyone up, you may need to use the odd flash/binding/greater on the tank according to the damage his taking
Keep telling people to use lightwell, its prob the most effective heal we have ticks for 7k a go roughly with your spell power.
Dont spam renew, it's hardly ever worth the mana cost in the new dungeons, things hit hard and fast, generally i only put a renew on the tank or if i MUST move.
Prayer of mending, love this spell, get it glyphed keep it on cooldown, it is one of the best spells a priest has, as soon as i got used to keeping this on cooldown people pretty much stopped dieing.
I found a priest to be a fair bit of learning over my shaman, you need to judge a lot better when damage is comming and swap between HW: S/heal to greater heal accordingly to keep tank/people topped off as needed.
Be warned tho, if people are taking hits from easily avoided stuff, you will struggle to keep them up regardless. I had a tank on the dragonhawk boss take 3 ticks of flame breath 5 times in a row, needless to say it was harsh on my mana.
Keep at it once you get used to the healing style and the right decision making it gets a lot better, personally i have gone for haste in the new heroics and it's worked well for me, typical aoe fights im healing about 15-16.5k hps normal encounters are 10.5-11.5k hps (when i first started my average hps was low at about 9.5)
Goodluck and i hope my own efforts to improve help, but be warned as much as i have tried to read up and adapt, some of my rotations might not be accurate, they are however working for me.