When it comes to World of Warcraft, there are so many different ways that you can get the experience you need in game - from killing mobs to questing. Each offers different types of experience points and each one is done differently. So, you need to know the basics of getting the experience you need in World of Warcraft as quickly as possible so that you can get out of the starting zones and really start to level like crazy.
You want to have a good combination of both questing and grinding (killing mobs) and the vast majority of the quests in the starting areas of the game will allow you to do that. You will also get some experience points from exploring, and even though they aren't much, you want to make sure that you explore all of the starting areas (and all of the areas in the game that you are in) so that you gain those xp points and you fill out your maps as you go. I personally don't recommend just grinding your way through the game, as you'll get really bored really fast and you will find that you miss out on some special items that you can only gain from questing. So, start off by gathering up the quests that are available to you when you hit the starting area. This is usually only one or two. Do them and then head back and turn them in - but as you go, you want to grind on mobs along the way back to help up your xp. When you turn in those first quests, make sure that you pick up all of the quests that are now available to you, as you should have three or four. Do them all and grind your way back. Turn them in and continue on this way until you have finished up all of the quests in the starting areas of the game. Don't skip any of the quests in these starting areas, as they are all super easy and there is no reason to skip them at all.
This is the easiest way to level throughout the starting areas. Make sure that you do all of the quests available to you and grind your way back when you turn them in. It will also gain you enough loot to sell to buy extra bags before you leave the starting area and up your gear as well.