Level 1-5
If you are an Orc or a Troll you will start out in the Valley of Trials. Take your first quests from the people nearby and chack back regularly when you level for new ones. Most of your quests will have you going north to face agents of the Burning Blade.
If you are a Tauren you will start out at Camp Narache. Get your quests from the villagers and head out to level. This is by far the most spread out starter zone so be prepared to do a great deal of running.
If you are a Blood Elf you will start off in Eversong Woods on Sunstrider Isle. Your first quest will teach you how to use your racial abilities Mana Tap and Arcane Torrent and more quests will follow. When you return from your quests in Falthrein Academy head south east to the Ruins of Silver moon.

5-10
If your are an Orc or a Troll leave the valley and head east. Follow the road east until it bends north and head south to Sen'jin Village. Load up on the quests here and when you are done head north to Razor Hill.
If you are a Tauren follow the road north to Bloodhoof Village. Set your hearthstone here and start questing. Once again, you will have a lot of distance to cover. Eventually your quests will lead you to more on Thunder Bluff.
If you are a Blood Elf accept the delivery quest from the NPC at the gate and follow the road south towards the inn. Set your Hearthstone here and accept the few quests here. When they are finished follow the road west to the West Sanctum. Do the quests here then follow the road down south to Fairbreeze Village and load up on the quests here.
11-15
If you are an Orc or a Troll finish up any quests you have in Razor Hill and head west into the Barrens. Keep following the road until you reach a town at the Crossroads. This will be your quest hub for a long time so set your hearthstone here and load up on quests.
If you are a Tauren finish up any quests in Mulgore and head east from Bloodhoof Village and trek north through the Barrens. Make sure to get the flight path at Camp Taurajo along the way. From this point on you will be leveling with the orcs and trolls.
If you are a Blood Elf finish up any quests you may have missed in Silvermoon city and head south into the Ghostlands. Your first order of business is to follow the road south until you come to Tranquilian. This town is a separate faction from the Horde with lots of useful reputation rewards. Each quest gives you tons of rep and if you complete them all you will be exalted and be able to buy a rare quality cape.

15-20
If you are in the Barrens head northwest to the stonetalon mountains. There should be some quests from Ratchet and the Crossroads here for your to complete and you can get the flight point for Sunrock Retreat. When you are done head south to Camp Taurajo. This will be your next quest site for the remainder of the Barrens.
If you are a Blood Elf finish up any quests you still have in Tranquilian to get your cape then head to the eastern side of the mountains to Farstrider Enclave. This will be your next big quest hub so load up and finish them off. When you have finished the quests here head south between Tranquilian and the Enclave to the Sanctum of the Sun. There are a few quest givers here that will round you off to level twenty.
20-25
If you are in the Barrens Continue on with the quests here at Camp Taurajo. At level twenty three all the horde races should be leveling in the same places. If you were in Kalimdor head across the ocean and travel to Tarren mill in Hilsbrad.
If you are a Blood Elf head to the Undercity through the Transporter orb and then south along the road into Tirisfall Glades. Halfway down the road there is a path that goes right to a flight point and quest hub called the Sepulcher, but most of the quests here are green or lower. There may be one or two yellow ones here so you may want to take them if you are not yet twenty. Either way, when you are done continue south and then left to Hilsbrad. Follow the road until you get to Tarren Mill. Set this as your new Hearthpoint and do the quests here.
25-30
Hilsbrad will last you till about level twenty seven, at which point I took the blimp from Undercity to Ogrinmar and then hiked over to the Stonetalon Mountains. Halfway up the pass is a horde camp called Sun Rock Retreat. Make this your new base and take up any yellow quality quests. There will only be a few since this is another twenty to twenty five zone. When there is nothing left here go south through The Barrens to Thousand needles. Halfway through the zone is Free Wind post with more quests for you to take on. This should take you to thirty.

30-35
Keep questing in Thousand Needles until level thirty one. Then fly back to Sunrock Retreat and hike through the mountains to Desolace. Now your leveling will start to take you along a similar path as the Alliance. In the center of Desolace, north of the Kodo Graveyard is Ghost Walker Post, a Horde quest hub. Another hub with an inn is Shadowprey Village along the southern coast.
35-40
At thirty five head to Brackenwall Village in norther Dustwallow Marsh. This will easily take you up to level 40. But I would sugest taking a break at level 37 and doing the quests at Hammerfall in the arathi highlands, or Grom'Grol in stranglethorn. When you are done head back to Dustwallow and finish up any quests until level forty.
40-45
After you get your mount you have a few choices on where to level. You could go to Feralas, Stranglethorn Vale or the Badlands. All of these areas have enough quests to easily get you to level 43. At 43 head to Gadgetzan in Tanaris and make it your base. Load up on the quests here and when you are done you should be nearly 45.
45-50
Travel east to Steamwheedle port and take on all the quests in the pirate base to the south. At level 47 head to Ashenvale and go north into Felwood. Near the Emerald Circle camp is a Deadwood Furbolg base for you to grind on. At forty eight take the quest from the friendly Furbolg NPC to collect feathers so you will achieve unfriendly reputation with Timbermaw Hold. When that has been completed head back to the Emerald Circle camp and take on their quests. This should get you close to forty nine. Head south to marshals refuge in Ungoro Crater to finish off your level.
50-55

Finish up any quests in Ungoro and leave at fifty one. Head to northern Azeroth and the Western Plaguelands by flying to Undercity and going east along the road to The Bulwurk. Load up on the quests here, but

there is no inn in this zone so you should max out your rest and log out in the open when you need to quit. If you run out head back to un goru or go north to Winterspring.
55-60
Finish up any yellow quests in the western plauglands and take the road east. Keep following the road until you near an abandoned town Called Corwin’s Crossing. Go around it and keep heading north and east until you get to Lights Hope Chapel. There will be plenty of quests here that should get you up to level 58. If not head back to winterspring and finish any quests there. When you have hit 58 you can enter outland.