How do I heal in a mana-efficient way as a Smite Discipline Priest?

Allow me to preface this by saying that this is not coming from personal-playstyle experience, but leading raids and watching / working with the priests in my guild that run Smite spec, I have a good amount of observation.

First and foremost, your most efficient heal is through Atonement procs. Simply spamming Smite is enough to keep most tanks topped through regular damage. Take note of the 15 yard range requirement on Atonement, however. If you're trying to heal up a group/raid member and they're not within 15 yards of the target that you're Smiting, they're not going to get healed. As LessPop_MoreFizz mentions in his comment, you're replacing Heal with Smite, and relying on the 15 yard range rule. It requires a bit more spatial awareness in that you need to know where your targets are as opposed to just yourself. Heal is certainly less effective, but should still be your filler spell (besides Penance) when targets are out of range or you absolutely must heal a certain target right then and there. Also, you should definitely be running with the Divine Accuracy Major Glyph, as that essentially makes it impossible to miss with Smite on any Boss level target.

Secondly, you should note some of the big interactions with your spells:

• Penance is great for burst healing and quickly getting Grace stacked on a target.

• Power Word: Shield, as you mentioned, is important due to Rapture procs, and managing these is key to your mana management.

• Prayer of Healing remains a strong group heal (not only with just Inner Focus) especially so as Disc, since you auto-proc your Divine Aegis shield off PoH regardless of crit vs. non crit.

• Power Infusion is considerably stronger when used on yourself as a throughput cooldown. In the past, it's been reserved exclusively for mage/warlock types, but it's perfectly viable to use it on yourself now. It's practically a "use when up" spell due to it's relatively low cooldown.

• Healing your Weakened Soul targets with FH, GH, Heal or Penance results in higher crit chance, not only proccing DA but also Inspiration. Note that this does not include the Atonement heal, so if you're vehement about keeping Inspiration up, watching Weakened Soul is a very good way to help maximize uptime.

Generally speaking, while popping Archangel is great for your mana, note that Evangelism actually increases your damage done by Smite and reduces the cost of both it and Penance by more than Archangel provides overall. If you're looking for instantaneous throughput, it's oftentimes better not to pop Archangel. However, for prolonged throughput and mana effeciency, you definitely should. That choice is obviously reserved for your feel of the current fight and how much effective healing you need.

Binding Heal, Greater Heal and Flash Heal all have their place, though they're certainly a bit more niche as Disc.

• Greater Heal is still your largest single target heal, and capable of being spammed, which edges it out above Penance ever so slightly if your tank is taking continuous large hits. That's not to say you shouldn't be mixing them together, but rather that you can't chain Penance back to back.

• Flash Heal is still good if someone needs a rapid heal to avoid dying in the next 2 seconds, and you know that they wont survive without a good amount of health in a short amount of time. The raid encounter Chimaeron in Blackwing Depths is a perfect example of fights where this is often utilized.

• Binding Heal is your throughput go-to when there's a good amount of damage going out but you're focusing on getting a certain target back up. It's effective in smaller groups like 5 mans, or raid fights where you're supposed to split up. Nefarian phase 2 comes to mind. It's not mana efficient, but it's great for getting quick health to two targets at the same time, and it's overall more efficient than Flash Heal.

Lastly, as an overall word about Cataclysm healing. The healing game early on is a lot more about teaching you how to play triage and get out of the Wrath mindset of "heal everyone to 100% in the next 2 seconds". If a player is at 25% health, with 0 chance of taking damage in the next 10 seconds, but your tank is at 70% and taking constant damage, you pick the tank. Mana regeneration and spell costs for fresh 85 characters is rather punishing, admittedly. If you're having trouble maintaining your mana pool, however, ask yourself these questions:

• Can I get more spirit somehow? Gems, reforging, elixirs, etc.
• Am I using mana potions when necessary?
• Am I using all of my helpful CDs? Pain Suppression, Power Word: Barrier, etc.
• Is my tank using his CDs? Shield Wall / Barkskin / Divine Protection / Icebound Fortitude and any other number of tanking CDs they have.
• Are my DPS taking damage from things they shouldn't?

A special note for the last point there regarding DPS taking damage. As noted, gone are the days where healers can heal through stupid mistakes. If DPS are taking damage to things that they can be moving out of, avoiding, or that they can prevent (like interrupts, using CDs of their own), it's little that you can do to help.

I know some of these last points were more generic than specifically focused on Discipline spec, however I feel that they're important to note since it sounds like there are some general issues in progressing from normals to heroics (and logically, subsequently, to the raid scene) where each "tier" gets progressively stricter in performance, gear and knowledge requirements.