Druids have 3 primary healing spells:
Rejuvenation: Instant-cast healing over time (increased healing
with talents)
Healing Touch: 3.5 second cast large heal (3.0 seconds with
talents, lower casting cost with talents)
Regrowth: 2.0 second cast moderate heal and moderate healing over
time. HoT stacks with Rejuvenation (large crit rate with talents).

With that being said, I never use Regrowth. Why? Because the mana
efficiency is terrible, and it's too hard to anticipate a party
member's needs with it. To make things even worse, the Regrowth
talent crit ONLY affects the first half of the Regrowth healing,
not the HoT part. The only time I would use Regrowth is if I
absolutely needed to heal someone ASAP, and already burned my
Nature's Swiftness.

I have max Rejuvenation 10, Heatling Touch 10, Healing Touch 6,
and Healing Touch 4 on my hotbar. This is the role of each spell:
Rejuv 10: HP topper, something I can quickly cast on multiple
party members in a row.
Healing Touch 4: this one actually is .5 seconds faster to cast
than the higher levels. It is very cheap and I consider it a freebie.
Healing Touch 6: my main spell. Generates little threat and heals
~1000-1200 HP, making it easy to time.
Healing Touch 10: the big heal for when someone takes a lot of
damage. Also the only thing used with Nature's Swiftness.

The most important part of being a healer is sensitivity to party
needs. It's anticipating who will take damage when, and how early
to start healing. Since Healing Touch takes 3 seconds to cast, you
have to know how early to start casting it.

PROTIP: Let's say I'm healing Galtar, and punch Healing Touch 6.
While I'm casting HT6, I switch targets to Kriala, who has
suddenly taken a lot of aggro quickly. The MOMENT that HT6
finishes on Galtar, I can immediately punch HT6 again to start
healing Kriala. I call this "pre-targeting." to make a long story
short, change to your next healing target during your casting
time, so you can immediately hit your next spell ASAP.

Nature's Swiftness: NS makes your next Nature spell instant cast.
You can insta-root and insta-hibernate with this spell, but the
main use for it is Healing Touch 10. If someone takes a lot of
damage quickly, and I believe they will not survive the 3 second
casting time, I punch NS, HT10. Ideally, you will never have to
use it, but realistically, I use it a couple times per raid. I
have placed HT10 next to NS on my hotbar for this exact reason.

Innervate: Innervate greatly increases your spirit mana regen.
It's awesome for long battles. Since you can cast Innervate on
anyone, make sure to target yourself first by hitting F1 or by
clicking on your icon in the upper left. You can also Innverate a
friendly priest if you think he's a better healer than you. Be
careful, as every druid has a story about accidentally Innervating
a warrior.

Druid ressing: This one is a doozy. Since druids have a 30-minute
cooldown combat res, they cannot really save wipes. Hence you
should generally group with a primary resser like a paladin,
priest, or shaman. I use combat res when someone has died
prematurely in a battle, especially a MT or healer, or as a
last-ditch effort when we're about to wipe. Combat ressing a
warrior to finish a boss fight is extremely satisfying, especially
when the rest of the party wiped and would have had to start over.

Mana management: Druids have slow-casting heals, meaning they are
essentially going to constantly be in a state of casting. This
makes spirit-based regen useless in long battles (unless
Innervated). To this end, I have about 43 mana/5 sec of mana regen
on Jaana, often at the expense of INT and SPI. While Jaana has
~4000 mana unbuffed, the mana regen more than makes up for it.
Jaana rarely need more than 5 water in any instance, and often can
regen full mana just by sitting down between pulls. Most
importantly, that mana regen works during casting, which
spirit-based regen does not. This keeps the healing coming during
battle, even without Innervate. For those who are curious, Jaana
has Jelkik's Talisman, Abyssal Leather Boots, Gloves, Belt, and
Pants of Restoration, Archivist Cape of the Eagle, Band of
Rumination, Lorespinner, Milli's Lexicon, and +4 regen enchant on
bracers for mana regen. I'd love to get a Mindtap Talisman, as
that would bring me up to 54 mana/5 seconds.

Aggro management: I highly recommend taking Subtlety, and always
asking Paladins for Blessing of Salvation. Since my mana regen is
already excellent, I prefer Salvation over Wisdom. This will allow
you to overheal a little without taking aggro away from the MT.
Regrowth seems to generate the most threat, while Rejuvenation
seems to generate the least. Healing Touch 6 generates relatively
little threat in comparison, which is another reason I use it so
much.

PROTIP: Faerie Fire doesn't break sheep, sleep, sap, shackle, or
freeze. Help out a bit when things slow down, will ya, the spell
is virtually free.

Plus healing: For a healer, +healing gear is more important than
+spell crit gear. The reason being that healing should be based on
your estimate of the HP you heal. Crits throw this off a bit and
are unreliable. I would worry about stats and mana regen before
worrying about +healing and +spell crit. Since most +healing gear
has terrible stats, I wouldn't really focus on it until you can
get really good +healing gear that has good stats as well, such as
Bracers of Prosperity, Cyclone Spaulders, Rod of the Ogre Magi, or
purples. That being said, I probably should have chosen the Mark
of Tyranny over the Eye of the Beast.

Typical raid sequence: If the MT is the bow of the party ship, the
healer is the anchor. The MT's job is to pull by shooting or
charging, while the healer's job is to bring up the rear while
holding the party back if he/she runs out of mana. Normally what
happens is the tank pulls, I cast Rejuv on him to offset initial
damage. I watch people hack away from afar. I might put Faerie
Fire and/or Insect Swarm on the MT's target if I have room to
fudge with mana and aggro, but that should always take a backseat
to healing. I stay as far back as possible, to avoid unpleasant
enemy effects like silence. If one person is taking most of the
damage, I punch HT6 or HT10 as appropriate. If many people are
taking a little damage, I spread Rejuvs all around and watch for
those taking bigger damage. I'm staring at everyone's lifebar the
whole time, since that is my job, mostly throwing out HT6. HT10 if
someone gets hurt fast. As the pull finishes, hopefully everyone
is still alive, and then I throw around Rejuvs and HT as
appropriate to top people off. If the pulls are going to be tight
(such as Abominations in UD strat), I start drinking immediately
when my water icon lights back up. If not, I sit down and wait for
everyone to do their things, while my mana creeps back up slowly.
I urge the MT to keep moving until I say stop. I only cast damage
spells and poke with my weapon if there is very, very low risk of
anyone dying.

PROTIP: Hit "V" to bring up enemy HP. Just do it. It's most useful
in instances, but it also has the side benefit of exposing the
real Jandice Barov.

The most important thing to remember about being a Restoration
druid is anticipation. You need to anticipate party needs, and
constantly be doing something. You don't have the benefits of
shield, fade, or flash heal, so you have to be more creative with
a smaller spellset. However, with some practice and timing, you
can easily outheal many priests. Remember, tanks and rogues are
counting on YOU, and enter into harm's way assuming that YOU will
take care of them.