Strengths & Weaknesses
Shamans come in a variety of forms, and can either be focused around doing great elemental damage, huge burst melee damage, or survivability through healing. They are exceptional one on one PvPers, and are the best offensive support in the game. Signature abilities, like Earthbind and Windfury can make your opponents hate you, and turn the tide of battle in your favour very quickly.
Elemental Shaman
Often seen in level 60 battlegrounds, but much more rare in the outside world and in lower level PvP. These shamans are excellent at doing good sustained damage from range, and still have significant healing power to provide support or heal themselves while being focused on.

Chain Lightning, Lightning Bolt and Earth Shock are the bread and butter of the Elemental shaman. You can either spec 31Elemental/20 Restoration for an offensive build with Elemental Mastery, or focus more on survivability by switching to 21 Restoration for Nature’s Swiftness. I prefer Nature’s Swiftness simply for its versatility, as you can use it to insta-cast a Chain Lightning or instantly heal yourself/an ally to full with Healing Wave.
An elemental build is best suited to larger scale battles, like AV, or to a lesser extent AB, where you can hide at the back and rain lightning down on your opponents. You can see some big numbers very easily on Chain Lightning, especially with all the talents that increase crit chance, and when combined with +damage trinkets you can cause devastation.
As an elemental shaman, you want to look for gear with +damage/healing firstly, and crit chance second. You can get a lot of crit through talents, so that should not take first choice over other +damage gear. The use of a shield is important, as it gives a huge amount of mitigation, and still contains good stats (although often less attractive than 1hers, this is made up by the armour and block a shield provides).
Enhancement Shaman
Very difficult to gear effectively, and reliant on random generators, enhancement shaman become less effective as you level. Windfury is one of the best buffs in the game, and combined with Stormstrike has a high chance to proc, but it is still very reliant on luck. As meleeers, enhancement specced shaman have to get up close and personal with their targets, so often take more damage. This is further accentuated by the fact that enhancement shaman will most always be equipping a 2her, and will thus miss out on the mitigation of a shield. If going for pure damage, an enhancement shaman will also miss out on excellent healing talents in the restoration tree, and will be very poor healers when need arises.

However, this is all made up for by the fun that is an instagib. With a lot of luck and some good gear, you can basically instantly kill cloth wearers, especially pre-60. Windfury+crit=huge damage to all but the most heavily armour opponents.
Stormstrike, the 31 point enhancement talent, is one of the key but misunderstood abilities an enhancement shaman relies on. It does not grant an extra attack, but rather resets your swing timer. This means that depending on your timing and the speed of your weapon, it can be very effective or useless. If you cast it right before you were about to swing anyway, it is wasted, but if you time it to cast immediately after you attack, then you are getting the best benefit out of it. On top of resetting your swing timer, it also debuffs your target, increasing their damage taken from nature spells by 20%. This means Earth Shock, Lightning Shield, and to a lesser extent Chain Lightning.
General Strategies
There are some key abilities that will always be used when PvPing on a shaman. Windfury, of course, is one of those abilities. It lasts 5 minutes, so watch the timer and don’t forget to reapply it, or you won’t be doing much melee damage.
Shocks are an essential element of shaman offence, and knowing which to shock to use when is simple but sometimes overlooked. Earth Shock interrupts casting, and causes a large amount of damage. This is especially useful against healing classes, or any caster in generally. Don’t waste your shock, because while it is cooling down you have no way to interrupt them (unless you are a Tauren). Save your Earth Shock for when they are going to heal, rather than using it to do damage.
Frost Shock is great for kiting, or catching runners. It does good damage, and is often used as the opening shock to slow down your opponent. The player will be immune to the freeze effect (and also the damage) after four applications. This will wear off after 15 seconds.

Flame Shock is your worst shock, and is really only useful against rogues. Use it to prevent them re-stealthing, unless they have already been hit with another spell that prevents stealth (such as any DoT or Hunter’s Mark).
Totems are often overlooked. The best totems, for PvP, are Earthbind and Grounding totems. Fire totems are cheap extra damage. Searing Totem is particularly useful, as it may cause your opponent to momentarily dis-engage from you to destroy the totem, which will give you time to heal or inflict more damage. You should always drop those three totems when engaging an enemy.
Another element of shamanistic PvP that players often seem to overlook is healing. With 5 points in the Healing Focus talent, you will avoid interruption from damage 70% of the time. It is one of the best PvP talents available, and increases survivability dramatically. Nature’s Swiftness is another excellent talent that will increase your survivability. An instant, massive heal can change the tide of battle.
Don’t neglect others when you are healing. A particularly effective combination is a warrior and a shaman, as the attack-boosting abilities of the shaman, combined with some healing, can make the warrior a killing machine. You can also add in some of your own damage through shocks and melee when not healing.
Macros
Nature’s Swiftness + Healing Wave
This will cast NS then instantly cast the max rank Healing Wave you have. You can switch out Healing Wave for Chain Lightning, Ghost Wolf, or any other spell you wish to instantly cast.
/cast Nature's Swiftness
/script SpellStopCasting();
/cast Healing Wave
/script if ( SpellIsTargeting() ) then SpellTargetUnit ("player"); end
Arena
Elemental/Restoration shaman are the most commonly seen Arena class, because they can contribute good burst damage, as well as backup heal when needed. With Natures Swiftness, a shaman can get of an instant Chain Lightning for some good damage or an instant heal if a player is about to die.

Restoration shaman make good secondary healers when combined with another class, particularly a paladin or priest. This allows removal of all debuffs bar curses, and you have the benefit of an offensive dispel and a defensive dispel, which the shaman lacks. Earth Shield will most likely be removed quickly, but should still be cast before the battle on yourself or whomever is likely to be taking the most damage. Lesser Healing Wave on single targets, and if you group is getting hit, Chain Heal, are the heals of choice here.
Enhancement shaman suffer from having a small mana pool and low survivability. While they can dish out some big damage quickly, they suffer by relying on lucky Windfury crits. They can be effective, but once they are out of mana they are basically auto-attacking warriors, and will have very poor healing potential to boot.
The strongest thing going for shaman is Bloodlust/Heroism. This is an amazing buff that will turn the tide in your favour significantly. Use this once the battle has fully begun – you want your whole team to get the most benefit out of it.