Quick Leveling Tips:
1) Completely ignore professions. They take a LOT of time and you can always go back later.
2) Completely focus on quests. Get all of the quests you can for an area and then keep working on one until it's complete. If you get multiple quests for a particular area (kill so many felsworn, get the widgit from the monument, gather the plant that grows in the area, etc), then track them all on-screen at the same time. Complete them all and cash them in at the same time.
3) When you log off, ALWAYS leave your toon in a city or an inn so that you build resting bonus for xp.
I'll put in my 2 copper too. Agree totally with #2 and #3. Re. #1, professions can definitely take a lot of time, but IMO don't neglect your gathering profession (skinning, mining, herbalism). You'll hate yourself later, because you'll have to go back to the newbie zones and grind them up - very boring. You can always run out later and mine up a stack of copper ore real quick to work on your blacksmithing, but it will suck if you're skilling up mining at the same time.
If you go this route, you don't have to focus on leveling your crafting profession per se, as that can take more materials then are necessary to maintain your gathering skill. At a minimum, keep your gathering skill high enough to gather where you're questing and gather when you happen to come across a node.
A good way to follow this approach is to take two gathering professions when leveling - usually skinning (because you gather from the stuff you kill - more convenient) and then either mining or herbalism. This nets you the most money as you progress, since you're selling everything you gather on the Auction house.
I'll add a #4) loot EVERYTHING - even the crappy gray items. Sell all your gray-quality items to vendors, and sell everything else you can't use on the auction house - even white-quality items.
The only deviation to the two gathering profession idea is if you eventually want to do enchanting. If that's the case, do it from the start. This is because you'll have to disenchant all the magic items you loot (unless you use them) to make the raw materials for enchanting. Since you loot magic stuff in the process of leveling, and earn magic item quest rewards you don't use, you can skill up enchanting as you go. I recommend that you don't do enchanting with your first character though. One makes a lot of money selling magic items they don't need on the auction house, and your character will always be broke if you're disenchanting all this stuff.
*** BUT ***
Personally though, I would highly recommend against speed leveling. Enjoy the quest stories. Read all the flavor text. Explore the nooks and crannies. Work on your professions as long as you're enjoying them.
You'll get burnt out and bored if you speed level. You will have to "go kill 20 boars" regardless of whether you're speed-leveling or not. The story behind why the cute boars must die will be the thing to keep you engaged though.
As long as you're doing your best to work on quests in geographic "clusters" like Bob said, you'll still level just about as fast as rushing through it. Most new players won't be skilled enough at a fresh character to speed-level it efficiently anyway.
Don't make it into a job - enjoy the game. Otherwise, by the time you get to level 40 with us, you'll hate it and won't want to play anyway. Priority one: have fun!