Shamans are great single target healers and really great raid healers circumstances permitting. Our only group heal, chain heal, depends very much on players being in close proximity to one another (range increasing in 3.2, yay!). Many fights the ranged folks will be spread out forcing single target heals for any raid wide damage. The melee group is usually in tight quarters except on bosses with really large hit boxes, but the tank/melee group is normally where chain heal is going to shine in a raid environment.
Chain heal is also a smart heal in the sense that it will triage the players most in need of heals and jump to them first if in range. It is also one of two spells along with riptide that will proc tidal waves, a haste effect on our two healing wave spells. This mechanic is going to change slightly with 3.2 where it will provide extra crit to lesser healing wave instead of a lower cast time. In either case we want to keep that up as much as possible so cast riptide liberally and chain heal when it makes sense.
So aside from the chain heal spamming that will often account for the majority of our heals we have our single target and tank healing. Our signature single target heal is our earth "poo" shield which should be kept on a tank or whoever is getting hit the most at all times. It is our most mana efficient heal and it tends to keep its target topped off with minimal additional heals for the most part.
While you are watching that earth shield make sure you have water shield on yourself and earthliving on your weapon. The mana regen from water shield is invaluable as is the bonus healing and additional heal over time effect provided by earthliving weapon.
Next healing spell in order of priority is generally riptide, use this first when someone needs a heal. It is a decent instant heal with a heal over time component great for tanks since the more hots on the tank makes healing less spiky. It is also very versatile in cases where you need a heal right away or need to top off another player (or even yourself) while focusing on healing another target. Druid familiars can think of it as an instant regrowth with a cooldown.
Then we have our boring heals, lesser healing wave and healing wave. Lesser healing wave will be used more often generally and when glyphed to be more effective on target with your earth shield it becomes your primary tank healing spell after riptide. Healing wave is generally reserved for emergencies or times where high healing throughput is required (I suppose that would also be an emergency).
Speaking of emergencies, we have two cooldowns for just those types of situations, nature's swiftness and tidal force. Nature's swiftness will turn our next healing spell (any of our spells except a rez really, but we are talking about healing) into an instant cast. This will most often be used with healing wave for a big heal, but can also be useful with a chain heal when a few people clumped together need a heal right away. The cooldown on this one is dropping from 3 minutes to 2 in the 3.2 patch which will differentiate it from the druid ability with the same name.
Our other healing cooldown, tidal force, is used in times where you are falling behind in heals and need to play a little catch up. It significantly increases the crit chance of your healing wave and chain heal for the next 3 casts. Can be used in combination with nature's swiftness to get off a big crit heal instantly, but I generally use them seperatly so I have one of them available more often.
A brief word on crits, they are our friends. So many shaman abilities proc on critical heals. A couple notable ones are ancestral awakening which will heal the player with the lowest health for a percentage of the crit heal amount and ancestral healing which will buff the targets armor for a few seconds. Don't go around stacking all crit on your gear though, we still benefit more from intelligence and spell power (MP5 is nice too).
And one last word on mana; we run out, a lot. Compared to other healing classes that is. It really only becomes an issue when heavy healing comes into play, otherwise for the most part I find myself with plenty of mana and even toss out some dps now and then. A combination of water shield and mana steam or blessing of wisdom and other replenishment sources provides a good amount of regen for all but the most extreme cases. For that we have a mana tide totem which will give us 24% of our mana back over 30 seconds along with anyone else in range. Not a lot, but enough in many cases. If you are lucky enough to have a druid along with you an innervate goes a long way.