As a new player to the World of Warcraft, I suggest you finding a good Guild to aid you on your journey through the many obstacles you will face though your quests. There are people everywhere inviting left and right, so being a little picky can go a long way. The first few levels are easy to go through by doing few quests; it is when you get to level 15 or close to level 20 when you will be spending more time to level up.

Around that time the quests will request more and more travel time. You will find yourself running back and forth to fulfill simple deliveries, they are worth the walk, think of it as free experience. Try to keep up with your quest list and get them done, because when you enter a new area you will find many new quests that will easily fill up your list.