Sharman Overview

The Shaman class was originally only available to three of the Horde races: Tauren, Orcs, and Trolls. Designed as a counterpart to the Paladin, the Shaman class was originally unavailable to the Alliance. This was said to create much trouble in developing both classes since they needed to be balanced against each other. The release of the Burning Crusade expansion introduced the Shaman to the Alliance through the Draenei while the Horde gained access to the Blood Elf Paladin, thus making it possible for both classes to be developed independent of each other.
In parties, Shamans make the quintessential fifth member; supplementing the others with powerful buffs (using their totems and shields) along with healing or damage on par with other, more specialized classes. Shamans have the ability to resurrect themselves once per hour (which can be reduced with talent points to once every 40 minutes) using their Reincarnation ability. In addition to its uses within a fight, this, in combination with their ability to resurrect other players, makes Shamans a viable utility for wipe recovery.

Weapons
Starting
Maces (1-handed)
Staves (2-handed)
Shields (off-hand)

Trainable
Daggers (1-handed)
Fist Weapons (1-handed)
Axes (1-handed)
Maces (2-handed)
Axes (2-handed)

Cannot useSword
(1-handed or 2-handed) Polearms Ranged weapons (wands, bows, throwing weapons, crossbows, guns)

Equipment
Shamans wear leather armor up until level 40, at which time they gain the ability to wear mail armor. Because of this, many shamans take up the leatherworking profession, which can make certain mail armor around the time they get the ability to wear it. Additionally, the Dragonscale Leatherworking specialization can make several mail armor items with stat bonuses that are very beneficial to the shaman class.
Shamans can use one-handed maces with shields and staves by default, and can train daggers, fist weapons, and one-handed axes at a weapon master. In addition, since patch 2.3 shamans can learn to wield two-handed axes and maces by visiting a trainer, and, post patch 2.0, to Dual Wield.
After reaching level 40, a shaman can learn to wear mail armor from their trainer. For shaman casters, the Turtle Scale Mail available from Leatherworkers is good, other items such as the Chain of the Scarlet Crusade are better for melee shamans.

Elemental
The Elemental tree focuses on the shaman's offensive spell casting ability. It decreases the mana cost and casting time of spells while increasing their damage and critical strike chance. The 31 point ability is Elemental Mastery, a self buff usable every three minutes that gives your Frost, Fire and Nature spells a 20% increased critical strike chance and reduces the their mana cost by 20%. This buff lasts 30 seconds. The 41 point talent is Totem of Wrath, which increases the whole raid's spell power, and makes any enemies in its radius more likely to be critically hit.
Overall, Elemental is the best build for shamans who want to maximise their damage output in PvP. In raids, elemental shamans are more of a general utility class, so raid spots may be a little harder to find. In 5-Man instances and PUGs Elemental Shaman bring great flexibility and utility capable of high dps, buffing and healing (due to excellent spec and equipment synergy).

Enhancement
By spending talent points in Enhancement, a Shaman greatly increases melee damage output. This is a very appealing tree to lower-level shamans because dealing melee damage does not cost mana. At level 40, the Dual Wield weapon skill can be learned. Together with the infamous Windfury Weapon buff, an Enhancement Shaman's melee damage output is second only to Rogues and DPS Warriors. Together with their new 51 point talent, Feral Spirit, Enhancement shamans can quickly destroy a group of enemies while soloing, and bring a lot of DPS in to raids.
Enhancement builds generally have the highest damage output potential of all Shaman builds. In raids, enhancement shaman are highly desirable because their buffs to the other melee damage dealers are substantial. In PvP Enhancement Shamans usually have problems due to low survivability (compared to plate-wearing classes and Rogues) and susceptibility to Snares.

Restoration
The Restoration tree focuses on the Shaman's healing capability, reducing the casting time and mana cost of healing spells, while increasing their effectiveness. Restoration Shamans are well suited for any healing situation in the game. On top of that they offer good utility (like Mana Regeneration by Mana Tide Totem), and the best multi-target heal spell in the game (Chain Heal). The 41 point talent Earth Shield acts as a very mana-efficient single-target HoT with a long duration.
This tree is highly useful in PvP and group PvE, the only drawback being the rather low damage output, so solo play is more difficult. In return, a Restoration Shaman hardly ever dies while questing/soloing.

Attributes
This breaks down specifically for shamans as follows

At level 70, it takes 40 agility to gain 1% to critical strike chance.
At level 70, it takes 22 critical strike rating to gain 1% to critical strike chance.
Your level's worth of agility will increase your chance to dodge by about 3% (e.g., +60 agility will give a level 60 shaman +3% to dodge).
Every point of agility provides 1 melee attack power (e.g., +70 agility will give any shaman +70 AP). This means that every 14 agility provides 1 additional damage per second (e.g., +140 agility will give any shaman +10 DPS).
Every point of strength provides 1 melee attack power (e.g., +70 strength will give any shaman +70 AP). This means that every 14 strength provides 1 additional damage per second (e.g., +140 strength will give any shaman +10 DPS).
Every point of strength increases the amount of damage you block with a shield.
Every point of intellect adds 15 mana (MP).
Your level's worth of intellect will increase your chance to crit with spells by about 1% (e.g., +60 intellect will give a level 60 shaman +1% to crit with spells; at level 70 it takes +70 int.)
Every point of stamina adds 10 health (HP).
Every 10 points of spirit regenerates 1 mana per second. This can also be described as "five spirit yields 1 mana per tick" or "2 spirit restores 1 mana per five seconds" (MP5). See also Formulas:Mana Regen.
Every 18 spirit increases health regeneration by 1 health per second (i.e., 9 spirit restores 1 point of health per tick).
Every point of Intellect provides 1 attack power with the talent Mental Dexterity (e.g., +70 intellect will give the shaman +70 AP)

End-game expectations

Totems are a major part of the end game and knowing what totems will benefit the shaman's group members best in different situations is all part of the strategy involved in playing a Shaman. With the versatility that comes with a shaman you will always be the one patching up on various issues that your group might run into. If your party runs into an encounter which is very DPS heavy, you will find yourself supporting DPS, occasionally throwing in a Heal if needed. The same goes for encounters that require lots of healing.

A shaman's role in parties and raids will vary depending on how they choose to spend their talent points and equip themselves, as some of the shaman's versatility is diminished if they focus heavily on one tree. For example, a shaman who has specced Enhancement (and geared accordingly) may have problems healing, due to the lack of crucial intellect/+healing/MP5 bonuses on their gear which Restoration requires, but will greatly enhance melee group DPS in raids (enhancing warriors, rogues, and feral druids via Windfury Totem, and all physical damage classes via Unleashed Rage and Strength of Earth Totem). On the other hand a Restoration shaman gets very little benefit from going melee due to the lack of +hit/+Attack Power, whereas Elementals shamans can cast ranged DPS and still cast the occasional support heal, still getting the bonuses (in most cases) from +heal/+spell damage.

Leveling/Solo PvE Enhancement

It's the designers stated intent that Enhancement is the default leveling spec for Shamans. It has little to no down time, and a high damage output. The important spells and abilities are Windfury Weapon, dual wielding, Stormstrike and Lava Lash. The drawback of this spec is that not only damage output is high, but also damage taken due to the close-in melee type of fighting. At higher levels, Maelstrom Weapon allows regular instant heals, which remedies this problem greatly.

Elemental
As the ranged DPS tree, Elemental can also be used for leveling. It's much safer since mobs usually are seriously damaged (or even dead) before they can hurt the Shaman, but has the drawback that it needs rather large amounts of mana, leading to high downtime.

Restoration
For the purpose of leveling or solo PvE, Restoration is a rather poor choice. The tree offers next to no enhancements to damage output, and therefore killing mobs takes a very long time. The extreme survivability granted by a pure resto spec is not really helpful - sure, Resto shamans are in fact able to solo mobs nobody else can kill, but it's not really practical to kill an elite 2 levels higher if it takes 10 minutes or more. Going restoration may be useful when leveling in a group environment (with many instances), but even when healing a lot, a hybrid Elemental/Resto spec is better overall than pure Resto.

Group/Raid PvERestoration
Healing was the traditional role for Shamans in all groups or raids. Over the years, the other specs have become viable too, but Restoration is still a very well liked specialization for raiding Shamans. Since 3.0.1, healing Shamans even got an interesting spell rotation (since 2.0 it had been mostly Chain Heal spam). At least one Earth Shield is still wanted by every raid.

Elemental
Elemental is also a wide supporter of groups and raids while also contributing major burst DPS. Other spell casters, especially Fire Mages, Boomkins, Destro Locks, and incredibly enough, Holy Paladins all benefit greatly from your presence. These classes depend on spell crit just like Elemental shaman, and they give it out in total of 8%, 5% from Elemental Oath and 3% from Totem of Wrath. These talents are only available to Elemental Shaman, making us friends among other casters. Elemental Shaman have become a rather large tool that raids depend on for the amazing crits, but also a tool to boost the overall damage of the entire raid, since Totem of Wrath also affects melee crit as well.

Enhancement
Enhancement Shaman are also big supporters in groups and raids. They can throw out the standard totems to boost parties and raids just like the other trees, however, thanks to Enhancing Totems, their totems buff a bit more than other shaman. This talent is in the tier one section of the tree, so the other two trees can grab it and be just as beneficial. The main buff they give is Unleashed Rage, boosting melee DPS a considerable amount. Not as big of a supporter as the other two trees, but still packs a punch in any raid or group.

PvPElemental
This tree has great potential to throw off opponents that are both melee, and casters. Elemental Warding will fend off up to 6% damage from all sources. Astral Shift will further reduce damage if placed under one of the conditions. Thunderstorm is an amazing way to fend of melee attackers for enough time to throw in a quick heal. Finally Eye of the Storm (Talent) will help when you are trying to get a cast in when there are multiple people on you. These damage reducing talents along with the high damage output will allow for a rounded PvP Shaman.

PVPEnhancement
This tree can be very fun to mess with people, especially when they are caught off guard. Toughness will reduce both movement impairing effects and a good amount of damage since Enhancement Shaman do not use shields. Static Shock will allow 9 charges of your Lightning Shield, therefore reducing the times you need to refresh it during a fight. Maelstrom Weapon will allow you to toss in some extra damage or a heal at a reduced or no cast time. Finally, Feral Spirit will make you much more intimidating. These wolves are your pets and are affected by Bloodlust. Jumping an enemy by surprise with both wolves, Bloodlust, and some high damage output with Windfury Weapon and both instant strike attacks, many enemies will feel very helpless and intimidated.

PVPRestoration
This tree definitely needs some work in order to fully understand how to use it in smaller PvP situations. In large battlegrounds, you would just heal a DPS to keep them up while running through opponents. However, solo PvP can be slightly less fun as little damage output makes you a vulnerable target to any DPS. Tidal Force will allow your next three heals to have a higher crit chance, allowing bigger heals when you need them. Nature's Swiftness will become your best friend when you have little to no health remaining and need that quick heal. Focused Mind will reduce many silence and interrupt effects that will be used against you. Nature's Guardian doesn't seem like much, but it procs more often then you would think, helping you to toss in another heal before getting killed.Earth Shield will more commonly be placed on you as it will help keep you alive. Finally, Riptide is our instant cast spell that will automatically heal us and place a HoT on our target, increasing survivability a lot more. This tree can be pretty hard to get used to, but once you get the hang of it, no one can stand in your way.