Leveling quickly in World of Warcraft is a daunting task if you're not properly prepared to take it on. Most WoW players all make the same mistakes when they level. Avoiding these mistakes can be a key to success to pass up your friends and leave them in a World of Dustcraft ;)
~Plan Your Leveling Spec~
Leveling quickly is all about efficiency. You can't be efficient if you're sitting to drink every time you kill a mob. Plan out a talent spec that utilizes mana, health, and travel time efficiency. If it decreases the downtime between mobs, it's a good talent that will help you level fast.
~Don't Level Professions~
This is a hard one for most people. Those professions can be time eaters! The only profession worth leveling for most classes is First Aid because it helps reduce your down time when killing mobs. Don't level professions and you will level faster!
~Don't Run Instances~
Pick up groups for instances (PUGs) can be a huge waste of time. Consider the time spent looking for a group, waiting for the group to fill up, traveling to the instance, waiting for the rest of the group to get there, waiting between pulls, recovering from wipes, rezzing players, etc etc... As you can tell this can be a huge time sink for the unsuspecting player. You can level much faster by soloing and possibly doing the occasional small group quest.
~Less QQ More Pew Pew~
You may or may not be familiar with this phrase. Basically, it means 'shut up and play the game'. While chatting relentlessly with people in trade chat may be fun, it's very counter-productive when you're trying to level fast.
~Avoid 'Grind' Leveling~
It's a common myth that grinding is faster than questing when it comes to leveling. This is patently untrue. Blizzard put the quests in the game for a reason -- they want you to do them! Not to mention the fastest solo leveling times in the world were accomplished by questing. Questing to level is how World of Warcraft is intended to be played.
~Use a Leveling Guide~
This is the big one. People who have never used a leveling guide have no idea what they're missing out on. It practically automates the process for you. When I used my first leveling guide I shaved days... literally days of /played time off of my leveling time. There are a handful of great guides available out there. I've placed links to a few of them below.