I've not raided this week so I won't give my own view of Ulduar, but I've read two really good healing guides and I'm inviting you to read them too:
Healing Guide to Ulduar, on the Munch LandBoth are 25-Man (aka heroic) views about healing, but they are still good pointers about Ulduar, for both 25-Man and 10-Man.
Paladin Healing in Heroic Hulduar, on World of Matticus
As for paladins, well, aoe damage and mobile healing isn't our forte, as you know. So expect to be "reduced" to tank healing again.
Now a few first basic advices, that you can find examples of in the guides I've linked.
Especially in 10-Man, use Beacon of Light on yourself to stay alive.That point could be the strongest change from "Nax style" healing. As being non mobile healers, we have to stand in the fire sometimes to toss that heal, and we're confronted to the choice of moving & surviving, or staying & dying. And in such cases, the first choice which is the obvious one, can mean the death of the character we are assigned to heal. That's were the bacon will save you and your assignement. Aoe damage and mobility in Nax were much less an issue, you will feel they are in Ulduar.
Keep up that Sacred Shield. Mitigation is the new deus of healing. Spikes are very common and very strong in Ulduar, Razorscale blue fire patches and fireballs will probably be the first ones you encouter. Disc priests obviously have the edge on mitigation and shielding, but even if it has been strongly nerfed, keep your Sacred Shield up on the player in danger of spikes (if you ues a fireball "tank" on Razorscale it will be him for example).
My last advice, try to hit that boss a few times with your mace/sword/stick to get some mana back. With judgement of wisdom on it, you should be able to get some good mana regen even if with only a few hits during the whole fight. Most bosses have phases in Ulduar, and some of them are less healing intensive and will give you the opportunity to do that. Learn your bosses and try to find the right times to get these mana regen hits.