Dungeons still give too much experience. Yes, I'll get some hate mail for this. But due to the way dungeons -- especially at some levels -- scale, along with experience buffs, the fastest way from 1-110 now involves grinding one dungeon over and over and over again. It's the equivalent of the South Park "Make Love, Not Warcraft" episode, only instead of killing boars, you're killing endless worms in Ragefire Chasm or gnolls in The Stockades.
Common methods of power leveling include doing only those quests which are most efficient in terms of experience over time, and analyzing the quests in a given zone so as to do them in the most efficient order possible. Remember, the idea of power leveling is speed and efficiency--you may wish to obtain an addon that will show you how much experience per hour you are gaining to test your techniques. Additionally, ensure your character's talent build is crafted for maximum endurance. You want as little downtime (walking, drinking, eating, crafting, typing, etc.) as possible.
Although WoW currency can be found through quests, fallen enemies or the dreaded "farming" process, doing it the conventional way is time-consuming. Considering the upcoming release of the Legion expansion pack in August of 2016, stocking up on gold is more important than ever. This way, you can spend less time farming and more time buying everything you need to tackle the next set of challenges.
Any decently geared 90 can complete a Pit of Saron trash mob run in 3-5 minutes. Each mob in the heroic version has a chance of dropping a Battered Hilt, which sell on the auction house for around 10k. Video guides will show the best route to take to pull all the trash mobs at once if you're a class with good AOE; other classes can simply pull less mobs at a time and loot as they go. While this method is a little less reliable than farming Vale-- after all, you're left to the mercy of RNG gods-- it has a higher chance of huge windfall because you could get a multiple hilts every run. Pull the mobs, burn 'em down, and cross your fingers when you loot. On top of the hilts, there's plenty of vendor trash, BoP epics for enchanters, and even a trinket that turns you into a gorilla. You will have to have completed the Forge of Souls in Icecrown Citadel to access this particular dungeon, though.
Once again, as soon as you hit 70 - I recommend to go and learn faster flying. This speeds up your questing A LOT, and is worth the time and gold. It will cost 4500 if you go to the capitol, or 5000 if you prefer Shattrath/Dalaran, because you will not have reputation with them at that point. This price will sadly be above what a totally new character can afford, if you don't have any Main. But you should go and buy flying as soon as you have enough money.
Many people have asked whether we recommend leveling as Enhancement or Elemental. There’s no definitive answer here; it depends entirely on your comfort, your gear options, and if you’re in a group or solo. Enhancement benefits more from Honor Talents in open world leveling, and Elemental has stronger AOE damage for mass pulling. Feel free to experiment with both specs.
Also note that power leveling is sometimes used to refer to paying someone else to level your character to cap as fast as possible (i.e. they power level for you); a distinction used by Blizzard is to refer to the paid leveling as "power leveling service." This behavior is against Blizzard's Terms of Service. Power leveling yourself, which this article covers, is perfectly acceptable.