How to Gear a Mage for Raids

Histi here, doing a commissioned guide to gearing a freshly-80 mage so as to be ready to walk into raids and pull your weight.
Disclaimer One: I am not an expert, I may make mistakes. If you want a perfect, flawless and mathematical guide, visit Elitist Jerks Mage Forum.
Disclaimer Two: You don't have to do any of this, it's all optional. Everyone should be able to play their class how they like. Having said that, this will be a guide intended to make your mage do as much damage as it possibly can. Deviating from it may make you do less damage, simple as that.

Talents and Glyphs (shown in the links)
Arcane centres around using Arcane Blast to build up the damage buff, then releasing either a missile barrage or an arcane barrage. Icy Veins is too useful to ignore, especially used when you have a large amount of mana. Always use Mage Armour. Use Presence of Mind only when you have three Arcane Blast buffs up, use it to fire a fourth, then a barrage.

Frostfire spec takes advantage of every single talent that benefits the spell Frostfire Bolt, and turns it from an average spell into a supreme one. Open the fight with Living Bomb, then stack Scorch, then FFB away until Hot Streak procs, and fire the Pyroblast. If Living Bomb is gone, put it back up. If Scorch is almost over, refresh it. Continue with FFB.

While deep fire, deep frost and hybrid elemental specs exist, they simply do not currently compete with the above two for pure damage. Blizzard have however stated that they intend to make Frost better for PvE, and Fire better for PvP, so hold your breath if you like!

Gear
I will try to give two options for each slot, but where I give only one that is because it is either hard to obtain or the only sensible choice.
CHEST- the Ebonweave Robe crafted by tailors. Lots of hit rating here, yum.
Heroes' Frostfire Robe for 80 Emblems of Heroism.

CLOAK- Wispcloak from Tailoring.

FEET- the Sandals of Crimson Fury, Exalted from Wyrmrest Accord.

HANDS- Ebonweave Gloves, again from Tailoring. Save up for the mats.
Gloves of Glistening Runes from heroic Nexus. Advantage of being an easy heroic with five emblems that you ought to be doing as often as you can anyway.

HEAD- The Hat of Wintry Doom. Tailoring. Don't be fooled by the fact that this is a blue, it is a damn fine item. Hit rating, a meta socket, easy mats. Every fresh 80 mage should treasure this (stylish!) hat. Note: for FFB spec, metasocket the Chaotic Skyflare Diamond; for Arcane, slot in an Ember Skyflare Diamond.

LEGS- Woven Bracae Leggings from heroic Halls of Lightning. This instance is tough, but the legs are worth it. Take some guildies, pugging this place can be a bit of a nightmare.

NECKLACE- Encircling Burnished Gold Chains for 25 Emblems of Heroism.

SHOULDERS- Dark Runic Mantle. This is a random zone drop in heroic Halls of Stone, so you can either run the instance a few times and hope it drops, or buy it off the AH, where it should be quite cheap. Again, a blue, but epic shoulders are hard to earn, and the stats on these are sweet.

WAIST- Sash of the Servant from heroic Azjol-Nerub.
Girdle of Bane from heroic Utgarde Pinnacle.
Plush Sash of Guzbah for 40 Emblems of Heroism if you get really unlucky with drops.

WRISTS- Azure Cloth Bindings from heroic Violet Hold. Easy to get groups for this, so should be easiest.
Cuffs of Winged Levitation from heroic Oculus. You'd have to be insane to go for this one over the VH one, but hey, the option is there.

WEAPON- Titansteel Spellblade if you're feeling wealthy.
Flameheart Spell Scalpel for Revered with the Kirin Tor, until you save up the cash.

OFFHAND- Ward of the Violet Citadel is the only real option here. 25 Emblems of Heroism.

RINGS- Signet of Hopeful Light from Exalted with Argent Crusade.
Annhylde's Ring from heroic Utgarde Keep.
Band of Guile from heroic Culling of Stratholme.

TRINKETS- Sundial of the Exiled for 40 Emblems of Heroism.
Darkmoon Card: Death will probably cost a bit of cash, but it's good.
Mark of the War Prisoner is a bloody good one from heroic Violet Hold.
Forge Ember is another good choice from heroic Halls of Stone.

ENCHANTS- Spellpower and Hit Rating on everything wherever possible; the headpiece can be enchanted with an Exalted Kirin Tor arcanum (but this is expensive; up to you whether to use it on the Hat of Wintry Doom or save it for an epic). You need a lot of Hit Rating; aim for around 200 if Arcane and around 290 if FFB or Frost.

GEMS- If not Hit Capped, gem for Hit Rating. If you are, gem for Spellpower. Socket bonuses are generally not that great; Runed Scarlet Rubies are your friends.

Maximum number of Emblems of Heroism required: 210
Theoretical average gold cost assuming all bought options selected: 3200g approx.
If there's anything else, don't hesitate to ask me in-game!

Using this guide, a fresh 80 mage pulling 700 DPS in heroics went to Ulduar a week later and pulled 2.8k. Get to work!