Priests are a versatile class. Other classes tend to have one area of healing excellence; priests can do well in almost any role. Holy specced priests will do best as area-of-effect healers; while Discipline specced priests excel as single target healers. As a general rule, holy priests will be assigned to raid heals and a discipline priest will be healing the tank or off-tank.
With dual specs now available, some healing priests will go with a dual spec of discipline and holy and will switch depending on the needs of the raid and the demands of the fight. Still, a shadow spec can make farming faster and easier and many priests will pick one healing specialization and take shadow as their second spec.
There is no one cookie cutter spec for either the Holy or the Discipline priest and you will need to play around to determine what spec best suits your healing style. There are a few mandatory talents: All priests will put 14 points into the Discipline tree to get the Meditation talent. It gives you mana and without mana, you're not healing. Most Holy priests will want Spirit of Redemption, Serendipity, Circle of Healing and at least one point in Holy Reach. Even if you only die on the rare occasion, Spirit of Redemption gives a very nice buff to your Spirit and is well worth the one talent point. You went holy to be a raid healer, so you'll want Circle of Healing, and Holy Reach increases the range of that spell and Prayer of Healing. Serendipity is a tool to increase your haste for GH and PoH. Many fights are quite predictable and, if you have Serenity procced and ready to go, can make your Prayer of Healing spell a fast cast spell when massive raid damage hits.
Allocate your talents as best suits your personal style. If you cast Renew often, you'll definitely want Improved Renew and Empowered Renew. If you seldom cast Renew, spend your talent points elsewhere. If you're a Holy priest who won't be using Power Word: Shield often, do not spend points on Body and Soul.
The big bread and butter spells for Discipline priests are Power Word: Shield and Penance. Power Word Shield mitigates incoming damage and is a fast cast spell, so Improved PW: Shield is a given. Penance is a powerhouse healing spell. Couple this talent with Aspiration, which reduces your Penance cool down. These two talents, together with Glyph of Penance, makes Penance an extremely powerful spell and the Discipline priest who wields it a powerful single target healer. Even with the nerf scheduled for 3.2, every Discipline priest will want this spell in his or her arsenal. Other talents the Discipline priest will find very attractive are Divine Aegis, Borrowed Time, Grace, Pain Suppression and Rapture.
The other primary spells you will use as a Discipline priest are Prayer of Mending and Flash Heal. You'll be pre-stacking PW: S and PoM on the tank every chance you get. You can use these two spells, along with Prayer of Healing to help out when a large amount of raid damage comes in as well.
Attractive Minor Glyphs are Glyph of Shadowfiend (restores mana if your shadowfiend dies early) and Glyph of Levitate (goodbye light feathers). Most will choose either the Glyph of Fortitude or Fading for their final Minor Glyph.
For Major Glyphs, popular glyphs for Holy priests are Glyph of Flash Heal, Glyph of Renew, Glyph of Circle of Healing, Glyph of Prayer of Healing and Glyph of Guardian Spirit. Which three to choose will reflect on your healing style. For Discipline priests, Glyph of Flash Heal is also popular, along with the Glyph of Penance and Glyph of Power Word: Shield.
For a Holy priest, your main spells are Circle of Healing, Flash Heal, Prayer of Healing and Prayer of Mending. Remember that your Serendipity talent will speed up your Prayer of Healing Spell and have a three stack whenever you anticipate incoming raid damage. Also, don't forget Hymn of Hope when mana gets low and Divine Hymn to deal with widespread raid damage.
For a Discipline priest, your primary spells are Flash Heal, Penance, Power Word: Shield and Prayer of Mending. Discipline even has a powerful AoE heal in Prayer of Healing. While not as powerful or fast as that of a Holy priest, it can still be valuable when raid-wide damage puts many in the danger zone.
Anticipation: Proactive and Reactive Healing
What separates the good healer from the great healer is being able to anticipate incoming damage and heal proactively. Many of the fights in Uldaur have predictable incoming damage. Learn the fights and have Serendipity 3 stacked ready to cast a hasted PoH when the Deconstructor throws Tympanic Tantrum or Kologarn casts Shockwave. Have the Renews ticking for Heat Wave in phase 2 on Mimiron and have PoM sitting there ready to start jumping. A Discipline priest will use Shield preemptively to mitigate incoming damage. Also know your fellow raiders. Are their members in your raid who are likely to steal aggro? Is the raid about the break a sheep? You might want to cast a PW: S on the mage who cast it. Tanks are good at grabbing aggro, but are not fail proof and mages are very squishy. Any healer can react to healing that is already done. The great healer anticipates incoming damage and starts to cast spells proactively.
What stats should you look for in gear? Intellect is probably your most valuable statistic for both Holy and Discipline. Crit is also important for both specs as is Spellpower. While the value of Spirit has decreased, it is still quite valuable to the Holy priest and of middling value to the Discipline priest. Stamina is also a valuable stat, but this statistic should grow at acceptable levels as your gear improves without any special focus. As a general rule, Spirit is a more valuable stat for the Holy priest than Mana per five, as it gives a boost to Spellpower as well as to mana regen.
Haste is more important for Holy priests. Elitist Jerks recommend that a Holy priest stack Haste up to 12 to 14%. Haste is less valuable to the Discipline priest and should not be stacked above 11%.
When you come to raid make sure your gear is enhanced with the proper enchants. For your helm, you will want to be Revered with the Kirin Tor to get the Arcanum of Burning Mysteries enchant or with the Wyrmrest Accord for the Arcanum of Blissful Mending. For your cloak, Enchant Cloak: Greater Speed (+23 Haste). If you are a tailor, the Darkglow or Lightweave Embroideries are additional options.
Enchant Chest: Powerful Stats gives +10 to all stats. The choices for bracers are Enchant Bracer: Superior Spellpower (+30) or Exceptional Intelligence (+16). The best enchant for gloves is Enchant Gloves: Exceptional Spellpower (+28).
A tailor can make Brilliant Spellthread or Sapphire Spellthread, which can be used to enhance pants. Good enchants for boots are Enchant Boots: Tuskarr's Vitality (adds +15 Stamina and minor movement speed) or Greater Spirit (+18).
For a one-handed weapon, the best enchant is Enchant Weapon: Mighty Spellpower (+63). For a stave, use Enchant Staff: Greater Spellpower (+81).
How you gem your gear depends on your needs and will change as your gear changes. The values to look for are Crit, Haste, Intellect, Spellpower and Spirit. Spellpower and Crit are always valuable, but at times you may with to boost your Haste to keep it in the recommended 12-14% range for a Holy Priest. There are also new epic Stormjewels, which give the highest pure stat boost. You'll probably want to save this for that special Best-in-Slot item, as these are rare and therefore quite expensive. You'll most likely be using the Insightful Earthsiege Diamond as the metagem for your helm.
If you anticipate high number of wipes as your work on new content, Flask of the Frost Wyrm is the flask of choice. If the wipe risk is not high, good Battle Elixir choices are Guru's Elixir (+20 all stats), Elixir of Spellpower (+58) or Elixir of Deadly Strikes (+45 Crit). Your best Guardian Elixir choice Is Elixir of Mighty Thoughts (+45 int).
You can use stat food to boost your Crit rate, Haste, Spellpower or Spirit. I personally tend to go for Crit, but will shift to haste if my gear changes bring Haste below 12%.
Be sure you come to raids with your gear fully and properly enchanted and gemmed. Bring sufficient supplies to keep your performance enhanced throughout the raid with flasks or elixir and food buffs. Also be sure to bring enough reagents to keep the raid buffed throughout the encounter.
Of course all this preparation brings us to actually casting spells, but that is a long post for another day.