What's the absolute fastest way to get a newly made monk to level 85 after Mists launches?
What's the absolute fastest (in terms of time spent after launch. Prep time pre-Mists is fine and can be discounted.) way to get a monk to level 85 and into relevant content when Mists comes out?
Use/abuse of XP bonuses from heirlooms, RAF, dual-boxing, etc. should all be considered fair-game here. Outright exploits and the hiring of third party players (aka power-levelling services) should not be.
Solution 1:
1-80
Level 1-80 can be done in a couple of minutes, you can choose any race except Pandaran, they are forced to do there starting zone and choose fraction so they will not work for this.
On a side note Pandarans get the racial Inner Peace, making their rested experience bonus last twice as long as normal. So a race change might be useful if you are not planing to go for max level in one go.
You will need to make a RAF account before MoP is released from your main account and use the RAF account to level up a combined 158 times. At least one character needs to reach level 80, so you'll need to buy WotLK for the second account as well. This will give you 79 levels to grant, so when you start your monk you can grant them all to your monk, instantly jumping to 80. There are a variety of ways to do this - the simplest is to just level two characters from 1-80, and then one more to level 2, but the consensus for 'fastest' seems to be that only leveling one character to 80, and then bringing up a few characters to level 20 or 40. The only things to keep in mind is that at least one character needs to reach level 80, and you need a total of 79 grantable levels.
Additionally, you should keep in mind that your progress towards next level as a percentage is retained when levels are granted. This means that before granting the levels, you should take the 10 minutes to grind your Monk 99% of the way to level 2. After granting 79 levels, you'll be at level 80, and a single quest completion away from reaching level 81, which makes a nice head start heading into Hyjal.
You can read more on the specifics of the level granting process, as well as optimal dungeon runs and dual boxing techniques for banking grantable levels in this thread at MMO-Champion. In particular, you'll want to make sure to take advantage of the 300% XP bonus for keeping your 'veteran' and 'friend' accounts grouped at all times while doing this prep work.
81-85
There are 2 ways that can be recommended, Dungeon leveling or tagging.
They share some preparation that you need a bit of gear and a Guild:
Gear
You will need heirloom that works for up to level 85, that is the helm and cloak, you can read more here on what heirlooms to get for a monk. Additionally, keep in mind that that your Monk is going to be wearing level 1 gear. Do yourself a favor and have a full set of Cataclysm-grade BoE's ready to go for your Monk before launch to keep yourself geared from 81-85.
Guild
You need a level 6 guild for the Fast Track (Rank 2) perk that gives you 10% more XP. Higher level guild is recommended to make life easier and you will need a level 20 guild for the heirloom helm. More info on what perks you can get can be found here.
Tagging
This consists of one playing attacking a monster and then one or more higher level player(s) killing the monster. The first player should receive full XP as long as the monster is not grey for the 2nd player. This can be very effective but can be mind numbingly boring, I have not done a lot of this so I cant recommend a place to do this, but what is important is the lower level player need to be able to attack the monster with out getting killed and there need to be a lot of monsters to kill, an example of a good place for horde players to do this can be seen below, as far as I can find this should still work(drops have been nerfed though) but I have not tested it:
Some level 80+ BoE gear would help the newly level 80 monk and a 2 person mount/guild summoning is also recommended.
Dungeon leveling
This is what it sounds like, running dungeons until you hit 85. Killing mobs in dungeons gives good XP and you get bonus XP from completing dungeons when signing up with the dungeon finder.
For this you will need a full set level 80 BOE Cataclysm gear (ilevel is important), but the Helm and Cloak do not have to be useful, you just need them to boost your ilevel since heirloom gear is ilevel 1(or 0 I forget).
Some blue level 80-84 boe items that a monk can equip(not necessarily useful, could be cloth) would also be recommended to make sure you keep your ilevel up even if you get unlucky with dungeon drops.
I would recommend running this as a full group(tank, healer and 3 dps) or at least tank+healer combo(the monk can be either of them if needed) to make sure you get instant queues. You can also do this with higher level chars(level 85 in full raid gear) to speed up the dungeon clearing.
Solution 2:
Aside from Refer a Friend, you can actually level to 85 pretty quickly from the guild perks and BoA gear. There's a bit more of a gold investment in game this way compared to spending money irl, but it's another options. There are leveling guides all over the place, but I found one on wowhead that was Monk specific (item lists, enchants to get, where to get food, etc).
My monk is at 77 and climbing...
http://www.wowhead.com/guide=1266/monk-to-85-in-3-days-played