Use Judgement more often
Holy paladins have two direct ways to restore mana: Judgement and Divine Plea. While Divine Plea has a few restrictions and use cases, Judgement (with Seal of Insight) simply works. Every time we use Judgement, we get back a portion of our mana. The more often that we Judge, the more mana we get back. With an 8-second cooldown, we can use Judgement about 7 times a minute. We have the ability to control our throughput by choosing a different spell, but mana is always the limiting factor. By Judging more often, we can net ourselves a significant amount of extra mana.
I like to review my World of Logs parses from past raids to improve my performance. To capture your logs for a particular boss or raid, just type "/combatlog" in when you log in, and the detailed combat log will be saved in your World of Warcraft folder under "Logs." What I do is take the total time of a given boss fight, and I figure out how many Judgements I could've squeezed in if I always used it on cooldown. I compare that against the number of Judgements I was actually able to use, and that tells me how many Judgements I missed over the course of the fight. I also check for when I Judged in the log browser to see where the lulls in Judging occurred. Sometimes we simply can't spare the global cooldown necessary to Judge, and that's okay.
Maximizing Holy Shock utilization
I analyze my Holy Shock usage in much the same way that I inspect my Judgement usage. Holy Shock is one of our most efficient heals, and HS generates a holy power point for us. Holy power releases are key to conserving mana, and so we want to generate as many holy power points as possible. Unless there's a desperate need to be casting a Flash of Light or Divine Light, we should be using Holy Shock on cooldown. You can figure out how many Holy Shocks you could've cast in a fight and compare that to your actual number of Holy Shocks to figure out how often you're using it.
Abuse your efficient heals
Holy Light only has one thing going for it: healing per mana. The spell is slow and weak, but it's incredibly efficient. If our targets aren't at any risk of dying, we should be using Holy Light instead of another heal. Bigger heals are less efficient and also introduce the risk of wasting healing to overheal. A great holy paladin will be able to identify portions of fights where raid damage is light and where it's heavy. With that knowledge, you can choose to use Holy Light to heal everyone up slowly instead of rushing to heal everyone instantly with bigger heals. A great example is during Magmaw's "down" phase: You have a full 40 seconds of zero incoming damage to bring everyone back to full life.
Holy Radiance can be used in a similar fashion, as it is easily our most efficient heal when the healing done is effective and not wasted. I'll often let everyone in my party or raid take some minor damage, waiting to heal anyone besides the tank, and then use Holy Radiance to heal up everyone at once. The situations that require everyone to be at 100% life are few and far between, and there's nothing wrong with letting people take some damage before healing them. Use the slower pace of Cataclysm healing to line up some very effective Holy Radiance periods, and you'll see your mana usage drop significantly.
Watch fight footage
If anyone in your guild records your encounters, I suggest watching the film. It's even better if you can record the fights yourself, although not everyone has a computer capable of that. I like to review videos of my past encounters, watching for the tips I've mentioned above. I watch my action bars to see where I forgot to use Holy Shock or Judgement, I watch for lulls in damage where I could've used more Holy Lights, and I watch for opportunities to use Holy Radiance or Divine Plea effectively. While fight experience is one of the best ways to get better at an encounter, there's nothing like being able to simply watch an encounter without worrying about actually playing. Great athletes watch film of every one of their games, and we can use their technique to improve our own game. As we really squeeze the most out of our various abilities, we'll see ourselves performing better than we ever have before.
The Light and How to Swing It: Holy helps holy paladins become the powerful healers we're destined to be. Learn the ropes in Cataclysm 101 for holy paladins, study the new balance between intellect and spirit and learn how to level your new Sunwalker. Tanking is a job, DPS is a craft -- but healing is truly an art.