So lately I've been doing a bit of healing in both raids and PvP. So I'm going to toss out what I'm doing and see what other more experienced healers have to say about it.
First off PvP, because if I put it second no one will read it...
Mostly it is keep rejuv up on folks. Anyone about to get focus gets 3 lifeblooms. Use swiftmend when you can. If you see someone running towards trouble/out of range, toss a regrowth on them. It lasts 27 seconds which is great for those durable dps you like to charge way out of range. In resilience gear, it is likely an equivalently geared DPS can not kill you if you can keep your hots up. Since you have 5 GCDs of hots to cast before getting to an interruptable spell, unless you are being actively dispelled, its unlikely that a dps who can interrupt is a problem. Though I'll admit I sometimes get hots up, cast an interruptible spell just so that I can then get a regrowth or two off after the interrupt runs out. In the event you are moving forward and getting in range of an injured folk, regrowth+rejuv is a really nice "have a chunk of health and 2 hots" that'll save most folk. And if the regrowth doesn't succeed in being cast, none of your hots would have ticked fast enough to save them anyway. Druid is a very mobile healer. Get used to healing and running all the time. Be comfortable with healing multiple people while running in lazy ovals to make it annoying for the melee dps to beat on you while also using nature's grasp. Remember you can shift out of snares and roots. Beware of warlocks banishing you. Keep in mind you can shift to tree form to escape and prevent polymorph/hex. Silence effects are our bane, more than stuns.
PvP gearing seems to be grab every piece of resilience+haste gear you can get, and then grab resilience+spirit. Gem for haste and spell power. You want 5% spell hit and ~80 spell penetration. Use blue sockets to get spell pen. Haste is pretty rare, so you'll probably only hit 300-400 haste. There are 2 talents you absolutely want in a pvp spec -- Improved Barkskin (keep most of your armor in elf & travel-cat) and Natural Perfection (take 12% less damage after people crit on you). You can actually fit these in to a PvE spec without much problem and have a completely reasonable/competitive PvE/PvP spec. If you are willing to sacrifice a little, you also want +20% range on balance spells -- its a big difference in both BG's and arenas having more range to throw CC.
PvE:
Raid healing: Rejuv everything. Wild Growth on cool down. Cast rotation is usually rejuv x5/wildgrowth/repeat. If they are taking enough damage, you want the rapid rejuvation glyph. If they are not, you absolutely don't. With the glyph you can probably cover 10 people. Without it 15. Use swiftmend if someone is about to die. Expect shaman to snipe your healing. If there are people who are taking heavier damage, regrowth and lifebloom can be useful but mana intensive.
Tank: Regrowth + rejuv. Nourish a bunch. Use wild growth if there is any raid damage - consider casting wildgrowth on the boss since it will hit everyone in melee range. Consider using lifebloom if you need more throughput, but let it bloom. Be careful with lifebloom because it can really suck all your mana fast. Glyph of Nourish, on a tank with a full stack of hots can be huge and really fast. I'm seeing 20k+ crits on a sub 1.0 second spell in ICC10man gear if I have all the hots up. Use swiftmend to catch up or to counter damage spikes. There is a pretty good chance that unless the tank is getting absolutely pounded you'll have some free cycles to keep a rejuv on yourself and other tanks/fragile healers or to wild growth a group. A druid can empty their mana pool if they want to -- its often a matter of pacing yourself appropriately for the fight. Just because you can be rolling a lifebloom and constantly spamming nourish doesn't mean you should.
Gearing: Get to 900 haste as fast as possible, then stack spell power. Spirit isn't bad, but isn't worth gemming for -- it is mana regen and a small amount of spell power. Unless you are wearing 4T9 or doing exclusively tank healing, crit rating is a very iffy stat. Even if you are doing exclusively tank healing, it is still somewhat iffy because Living Seed needs a hit to go off before it is consumed. And between talents adding crit (+25 or +28%) and boss swing speeds, there is a pretty good chance you'll have it already up.
Spec: There are 2.5 spec choices. First choice is: Will I have enough haste in my gear? If the answer is no, you can go with a sparser resto tree that gets you Celestial Focus from the balance tree. It'll be an 18/0/53 build. If you can get enough haste (figure over ~700), you'll probably want an 11/0/60 build (or 14/0/60 if you are doing exclusively tank healing - for anything but tank healing nature's grace is useless). The .5 choice is if you have enough haste gear and you want a move pvp viable spec, then you have to choose which of living seed or revitalize you give up to have the points free for pvp/solo'ing talents. I gave up revitalize because of my raid group and pvp team compositions.
Glyphs: There are 4 good glyphs. Nourish, Swiftmend, Rapid Rejuvenation, Wild Growth.
There are some situationally useful glyphs: Rejuvenation, Regrowth, Lifebloom, Innervate.
Nourish and Swiftmend are very strong if you are not exclusively a raid healer. People complain that the Rejuvenation glyph under performs, but it has the bit where it performs strongly when you need it most (+50% healing under half health). Wild Growth is considered a no-brainer for 25-man raiding, but I've not found it useful for 10-man. Regrowth is subtle in that it makes both the initial healing and hot 20% larger which can be significant for tank healing but means you want to be timing the spell to complete casting in the last 3 seconds before the last tick. In reality, I think you can make an argument for using a great number of combinations of glyphs depending on what you are healing.
Personally I am running with Nourish, Swiftmend, and Rapid Rejuvenation. I've run with several other combinations, but for a mix of 10-man raiding, heroics, and pvp that has seemed to be the optimal set for me.