Wand

A wand is a weapon that causes Arcane, Fire, Frost, Holy, Nature, or Shadow damage. They may be used by Priests, Mages and Warlocks. There is no restriction on the damage type that can be wielded and used; you can use wands outside your native damage capabilities. No class that can use wands needs to train to use them. (See the Per Class Proficiencies table for who can use what weapons.)

Before the 1.5 patch, wands were often berated by the caster community, who felt they were basically useless thanks to low damage per second. But with 1.5, wand wielders gained the ability to autoshoot wands, increasing their DPS to the amount listed in the tooltip. This greatly improved their utility -- but now you must stop autoshoot (see below) before casting spells.

Details

Wands are equipped in the ranged weapon slot, but they work at both ranged and melee distance.

They are fast, and will often outperform a caster's melee weapons at melee range.

Wands are also not affected by the [Disarm] attack.

Wands are not interruptible. Most of your spells are, especially at low levels. (However, wands may or may not cease firing if hit by a stun)

Wands use no ammo and no mana. They are typically used as a back-up for when you run out of mana. For low-level casters, a wand is often considered an effective means of killing a mob while saving their smaller mana pool for other spells, such as crowd control or healing.

Shooting a wand does not count as casting, which means that mana regeneration occurs normally for you, but also that they are not benefited by potions and buffs that increase spell power.

The relative value of using a wand vs casting diminishes as the caster gains talents that improve casting and remedy the same casting deficiencies that wands remedy (mitigating spell interruption, lowering mana costs, speeding up casting and cooldown).

Many casters prefer to carry two or more wands of different damage types to match up with the target's vulnerability. The Arcane, Fire, and Shadow types are more common than Nature and Frost types. Holy damage wands are especially rare and valueable due to Holy's nature of not being subject to resistances.

Higher level wands often have effects on attributes, resistance and spell power.

Wand Usage

To use a Wand

Equip a wand in your ranged weapon slot on the Character panel.
Move the 'Shoot' ability from the General Abilities tab of your Spellbook to a hot button on your button bar.
Target an enemy.
Push the Shoot button.

To stop using a Wand

To stop using a wand, do any of these:

Take a few steps in any direction, or jump.
Hit the Esc key.
Click the fire button again.
Right-click a mob (this should put you back into melee mode).
Re-target a mob by pressing 'T' (assuming you have the default key shortcut).
Activate an item.
Use a /stopcasting macro.

Sources

Most wands are drops or quest rewards. You will rarely see these at beginning levels. (The Blood Elf starting zone, Eversong Woods has a quest [11] Zul'Marosh that rewards you with the choice of a [Hoodoo Wand]. The Draenei starting zone, Azuremyst Isle has a quest [10] The Prophecy of Akida that rewards you with the choice of a [Stillpine Stinger].)

Most of first low-level arcane damage wands are made by Enchanters. These are one of the few items an enchanter can make and sell directly (these all Bind on Equip), so you should be able to find them in your auction house, often heavily discounted due to seller competition. These are all Uncommon Quality (Green) items, but note that unlike most green weapons, crafted wands cannot be disenchanted.

There are also Common Quality (White) wands which can be purchased from wand vendors. None of these is available to a beginning (Level 1-10) caster. As white items, these cannot be disenchanted, but they (all?) do not bind and can be resold or otherwise traded. There is a wand vendor in each capital city except Thunder Bluff and Darnassus, and also one in Shattrath City. (See Wand Vendors below)

Comparable examples of each kind:

Wands made by Enchanters

Wand Vendors

Ardwyn Cailen <Wand Merchant> in Stormwind City
Harick Boulderdrum <Wands Merchant> in Ironforge
Katis <Wand Merchant> in Orgrimmar
Muragus <Staff Merchant> in Orgrimmar
Oss <Wand Vendor> in The Exodar
Quelama Lightblade <Wand Vendor> in Shattrath City
Sydney Upton <Staff Merchant> in Undercity
Zane Bradford <Wand Vendor> in Undercity
Zathanna <Wand Vendor> in Silvermoon City

Notable pre-Burning Crusade wands

Mana-regen wand

These wands give varying amounts of +Mana/5 Seconds, and are welcomed by Priests especially. Examples:

[Thoughtblighter], a drop from Zul'Gurub
[Mana Channeling Wand], a drop from Dire Maul

Attributes-based wand

These wands have only attribute bonuses, such as Intellect, Stamina, and/or Spirit. Examples:

[Oblivion's Touch], a drop from Scholomance
[Stormrager], a quest reward from [60R] Order Must Be Restored and [60G] The Scarlet Oracle, Demetria
[Mar'li's Touch], a drop from Zul'Gurub

Spell-based wand

These wands have properties such as "Increases damage and healing done by magical spells and effects by up to xx." and alike.

Examples:

[Wand of Biting Cold], a quest reward from Alterac Valley
[Bonecreeper Stylus], a drop from Scholomance
[Pyric Caduceus], a drop from Blackrock Depths

Resist-based wand

These wands give little or no bonus besides a small amount of spell resistance. For example:

[Banshee Finger], a drop from Stratholme
[Torch of Austen], a random world drop
[Serpentine Skuller], a drop from Blackrock Spire
[Wand of Allistarj], a random world drop
[Flaming Incinerator], a drop from Zul'Farrak
[Gravestone Scepter], a quest reward from Blackfathom Villainy in Blackfathom Deeps

Hybrid wand

Such wands have properties from more than on category, and it is hard to clarify primary and secondary properties. Example:

[Antenna of Invigoration], a drop from the Ruins of Ahn'Qiraj

Wowpedia