First things first, you want to do quests until you hit level 30 before you start grinding.
Once you hit level 30 then go to Shimmering Flats and do all the kill quests and grind on the basilisks around the small lake to the south of the race way until you hit level 33-34.
From there if you have higher level help you can go straight to Scarlet Monastery and have them help you grind out that instance several times until you hit level 40. I find this way to be the quickest and best, but only with higher level help.
If higher level help isn't available you still want to do the Scarlet Monastery quests but don't waste your time trying to find group after group after group to do it over and over again as this takes way too much time.
At level 34 your next stop will be Stranglethorn Vale where you can grind on the Venture Co. Meteorologists at Lake Nazferiti. At level 36 you will want to go to Desolace, grab all the kill quests that have to do with nagas and then go swimming to the little island at the northwest corner and kill the nagas. Be careful though, you will want to watch out for the elite giant that wonders around in the area. Don't worry he only comes ever so often and is extremely easy to avoid.
Level 38-39, go to the Badlands and start grinding on EVERYTHING there. All the creatures are really close together and it is an excellent skinning area. At level 40 go to the Lethlor Ravine and start grinding on the whelps you find there. You can also skin these and you might get lucky and see a Tiny Black Whelping drop which usually sells on the Auction House for around 75-100 gold depending on the server.
At level 43 go to Tanaris and grind for the wastewander pouches which are carried by the humanoids in the WaterSpring Field. I don't recommend trying this unless you are on a normal server as you will get ganked a lot if tried on a PvP server. At level 45 go south along the coast into the pirate cove and grind there until level 49. There are a lot of treasure chests that spawn all over the place here so you can make a lot of gold here too. Don't forget to get the kill quests for this place!
Next stop is Raventusk Village in the Hinterlands. Grab all the kill quests and do them for really quick experience and you'll be level 52 before you know it! From level 52 you will want to travel to the Burning Steppes and grind on Firegut Ogres until you hit level 54. I would then go to Winterspring and start grinding there. A lot of good grinding spots exist here and are easy to find, so it would be pointless to list them all here. At level 58 grind at the Yeti Cave in Winterspring until you hit level 60.
Congrats, you made it! Of course, feel free to mix and match up these strategies with your own to make it a style you enjoy.
