When you start off as a level 1 in any area that you need to make sure that you do every single quest possible in your "newb area"... If you pick human you will start in northshire abby. Talk to all the people with the yellow question mark above their head. The newb mobs you will kill are behind your starting area. After you finish those head to goldshire it should be on the map. Now the idea of getting every single quest that you can at the time, is that some are collection quests which you do while you are on the main quests. If you get a delivery to storm wind don't do it until you finish the others. The lost guard quest and the elite trogg Hogger is where you should hit around level 8-10 or so. This should be about the end of quests for this area. Keep reading this alliance leveling guide for the rest.
Dwarf or Gnome you start in the same area. Basic run down pick up all the quests you can the newb mobs are back to the SouthWest just follow the road do everysingle one of these untill the only ones you have left are the delivery quests. Then go up to khranos and do those ones. When you finish Khranos head up the road to Steelgrill depot your quest log will give you directions. There is also Brewnwall village which you should do. Do everysingle one of these quests. You will need at least a 3 man group for the wendigos, frostmane hold, vegash.
Now if you were a human and you finished Elyyn Forest, you need to travel to Iron Forge. Take the gryphon to out of Stormwind city to there. Start on the quests in khranos.
If you started dwarf or gnome go to iron forge and take the gryphon to stormwind. Now do the quests in elwyyn..
Basically your leveling in the other races starting lands now the mobs your killing should be a little lower level than you so that you can cut right through them.
After you have done both of these. You will head to westfall or Loch modan. Do the lower level quests in these, DO NOT attempt the high level ones yet. As your trying to do quests that are around 1-3 levels below you right now for increased xp gain.
After you finish the tunnel rat ears and some trogs in Loch Modan go to West Fall and do some defias from sentinal hill. Also when you kill the harvest watchers there keep 5 flasks of oil, 5hops, and 5 okra as these are for other quests that you will get to later on.
Once the quests start getting hard in the loch go to westfall until they get hard and then go back the loch when the westfall ones get hard vice/versa depending on where you are at the time.
If you do go to redrige you can do a couple there at level 16-18 or so. Dragon whelps after you do a delivery to goldshire. Also kill some trogs there. The delivery quests make sure that you do these as 90% of the time they lead to other quests.
Also check out the Wow Mastery Guides as it includes a more detailed alliance leveling guide.
If you are night elf and want to get to the human or dwarf lands take a boat from darkshore to menethial harbor and you arrive in the wetlands. Make sure you stay on the road, and nothing should kill you. Run up to loch modan through the dun algaz gates.