I thought I would put together a basic guide on, "How to cast spells as a Disc priest." It can be counter-intuitive at first, having all these cooldowns on healing spells. So here's the basics:
1: Cast Power Word: Shield on the Tank
This may be obvious, as Disc talents practically beg you to shield people, but I have seen lots of Disc Priests who seem hesitant to shield the tank. I feel this is like a Fire mage not casting fire spells.
Let's be clear: Power Word: Shield is your first, last, best line of defense. You spent 11 talent points and a glyph on it (at least I hope you did), so use it! When you shield a tank, in addition to the 5-7k of absorption it adds, and the topoff heal from the glyph, you also give the raid a damage reduction buff and mega-haste your next heal. You want to shield the tank every time you get. You want their soul to be weakened permanently. These are Good Things (TM).
Some people might save shields for emergencies. This is silly: with Disc's talents you are far better reaping the great benefits from shields, and using Penance for emergencies. More on that later.
2: Cast Power Word: Shield on Everyone Else
So you're shielding the tank every 15.00001 seconds, what else? Well, you took Soul Warding to remove shield's cooldown, right? (Please say yes!) So cast shield on everything that moves! As Disc you can toss out a shield once a second, and with Ulduar's raid damage, this is very useful mitigation.
Check some wow meter parses if you like, but believe me, nearly all shields will get used. And with good situational awareness, you can shield those who pull aggro or eat random damage, saving them when no other healer can. And regardless, Rapture and Borrowed Time mean it's almost never a bad time to cast a shield. Throw at least one out in between shielding your tank, it will only help.
3: Cast Penance on Cooldown
Honestly, you could spend all your time shielding, and do pretty well, but you have other juicy talents to exploit make use of! Penance is an insanely efficient heal, and it heals a lot right away, so it's great to use on your tank.
In some cases it can be good to save Penance for damage spikes, but I recommend casting it on cooldown. With its short cooldown (You have reduced the cooldown, haven't you?), you can cast it often to keep them nice and full on health, and every time it crits it will add up nice Divine Aegis bubbles which will further smooth out damage.
It's nice to rotate spells so that after a shield, you cast Penance and then Flash or Greater. Penance benefits from Borrowed Time but doesn't consume it, so this way you get two lightning-fast heals.
4: Cast Prayer of Mending on Cooldown
So shield, Penance, what else... PoM! Disc doesn't have many talents to boost Prayer of Mending, but due to Ulduar's raid damage, in most fights PoM will be extremely useful regardless. So after a shield/Penance/heal cycle, toss PoM on a tank if it's available. It will always heal the tank, and bounce wherever it's needed. Many times it will bounce several times, which is free healing, and of course each bounce can crit and leave another small Divine Aegis bubble! We like bubbles!
Think of it this way: You shield a tank, Penance them to full and probably leave an aegis on them, then give them a PoM buffer. By the time a boss eats through all that mitigation and healing, your cooldowns will be up again and you'll be ready to do it again! And if the PoM goes on its merry way healing melee and other tanks, we're sure not complaining.
Conclusion
It can take time to get used to the Disc play style. Having all your major heals on cooldowns, and having one of them be channeled, is a new experience for a healer. But I feel the above guidelines are a good way to get your feet wet, to learn to use and love Disc's spells. If you need a concluding blurb to summarize all the above, it's this: The Disc tree makes Power Word: Shield and Penance into ridiculously powerful and efficient spells. The proper play style boils down to abusing using these spells for all they're worth!
Now go try it out, and don't rest until everyone in your raid is encased in a shiny golden bubble of safety.