The Basic Rotation
The basic rotation of an Arcane Mage revolves around the two phases, conservation and burn. The conservation phase is aimed at playing to the strengths of your mastery bonuses ie. keep your mana pool as high as you can to cause the maximum possible damage. You achieve this by wiping your Arcane Blast buff stacks regularly to balance your mana spent and your mana regenerated as best as you can. When you look at the talents and glyphs sections you see that a lot of selections are based on aiding this process either by boosting your mana regen or reducing mana costs of spells.
The other phase of Arcane Mages' rotation is the Burn Phase, so called because you are going to burn through your mana pool very very quickly with lots of pew pew "omg look at mah critz damage and dps" going on. Non-mages might call this your burst phase, but that's boring and we mages have a flair for the theatrical so we call it the burn phase. It reminds us of burning warlocks :P So what's the main condition for initiating a burn phase? Having your evocation spell off cooldown! With evocation available it means you can burn through your mana until you have roughly 35 - 40% left causes nasty nasty damage, you can then hit evocate and enter a conserve phase, safe in the knowledge that your mana pool will be roughly 95 - 100% full thereby once again maximising your mastery bonus damage. OK you could blow all of your mana in the burn phase, and that can be a good idea in certain situations (such as when you're certain the boss will be dead at the end of your burn phase), but in most cases you're going to be entering a conserve phase again and if you've blown all your mana in the burn phase you're only going to be getting a 60% of your mastery damage bonus. If you've played it smart, however, you'll be getting 95 - 100% of your mastery bonus damage. Don't let short term pew pew awesomeness blind you to being an effective DPS'er over the course of an entire fight. Remember what we said in the intro; you're a marathon runner, not a sprinter!
You'll also note that in the burn phase we're using all our non-mastery cooldowns and on use items, this is because we really want to maximise the amount of damage we're getting from our burn phase - it's where the largest chunk of our damage is going to come from in fights overall. Therefore try and build up those 4 stacks of the Arcane Blast buff, pop mana gem to restore mana and get a boost to damage (see the talent selection section) then get them cooldowns popped.
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Important Considerations For Your Burn Phase & Evocation
Aggro; make sure your tank has a firm hold on the boss aggro, the last thing you want to do is waste your burn phase because you're running away from the boss like a little girl. Even popping invisibility means you've wasted at least 4 seconds of burn time time (and all those cooldowns you popped) to drop the aggro.
Time your burn with Time Warp/Bloodlust/Heroism; your evocate spell may well be off cooldown but if you know that the raid leader is going to call Time Warp within the next minute or so hold off entering a burst phase so you can start burning when Time Warp is popped. A lot of Arcane Mages tie their haste soft cap around Time Warp (see the Stat Priorities section), doing that is pointless unless you're timing your burn phase with the Time Warp. Obviously if you're going for a higher soft cap because you're not relying on Time Warp then you don't need to worry about this so much. That's a personal decicion for you to decide depending on your play style, yes you'll sacrifice some mastery if you're going for the higher soft cap but play to your own strengths because that will increase your dps much more than just slavishly following a predetermined set of numbers because Simcraft simulations told you so. If you can't get the knack of timing your burn phase with Time Warp then go for the higher haste soft cap, at least until you know the boss fight well enough to get the timings right.
Situational Awareness, having none will fuck you up buddy; be aware of the boss's abilities and phases. If you remain oblivious to whats going on around you then you cans eriously mess up and waste a lot of opportunities. The most important is Evocation, don't evocate if you're going to have to interupt it by moving. This will leave you with no mana for the conserve phase, no mana for your next burn phase and still waiting for the evocate cooldown before you can really do anything about it. Similarly, although slightly less catastrophic, is wasting a burn phase. As mentioned earlier, Arcane Mages suffer in high mobility fights because they like to plant their feet and gets with the castings. If you enter a burn phase by popping your cooldowns and then you're forced to run about you're going to lose DPS. In some fights this is unavoidable, but as a responsible DPS'er in a raid team it's your responsibility to know the fight so you can at least try to time your burn phases during periods when you know you can stand still and nuke. You not always going to achieve that 100% of the time, but make the personal effort to minimise wasted burn opportunities, it will pay dividends to you in terms of sexy sexy DPS results.
If you want to go much deeper into this then the nice people at Elitist Jerks have complete tables on optimal spell rotations during different conditions. If you can translate it then good luck to you fella, you're doing better than I am lol.
Area of Effect (AoE)
I've already mentioned that Arcane Mages are weak at AoE gameplay and to be honest there's no real complexity here. If you're specc'd into Improved Arcane Explosion (see below) then try to build four stacks of the Arcane Blast buff then spam Arcane Explosion to your hearts conent. If you are out of position to use Arcane Explosion, then use the Flamestrike/Blizzard combination. This basically consists of laying a Flamestrike down underneath a target then casting Blizzard.
If you're not specc'd into Improved Arcane Explosion then I would reverse the above ie. try to cast the Flamestrike/Blizzard combination, if you're caught out and you're too close to the enemy then use Arcane Explosion until you can get some distance again. Remember you can use Frost Nova and Cone of Cold to root/slow enemies and Blink to gain some distance.
Personally, on small packs of mobs (3-4) that you tend to find in heroic dungeons I often find that you're better off following your single target converse phase rotation; no you're not going to match the DPS of that muti-shotting Hunter but that's ok.