To level in World of Warcraft, it is important to know where the best places are to level. It is also important that you do the quests in these areas, which makes it simple to level because you get the experience from killing monsters in the quest and the experience for completing the quest. Once you get to higher levels, you should try to complete all the quests in a certain area before you turn them in, so that you get enough experience to actually get somewhere instead of doing one quest, turning it in, and going back to the same spot to complete another quest. If you think about it, this would just be impractical and unreasonable and worst of all a waste of your time.
Tips in Case You Get Stuck on a Level
Try to beat as many quests as you can in one area so that you keep getting experience, don't just do the easy quests! The hard quests usually give you needed experience which can help you reach the higher levels.
If you can't find anymore quests in your favorite leveling spot; than you have either gone past the recommended level for that area, or you need to go to another area for your level to get new quests.
Tip: I find it helpful to switch areas every so often so that you never run out of quests and you have your level going up the whole time.
Another way to get up your levels when you get stuck is to go into cities and rest up so you can grind (kill lots of creatures) your way up the levels. This is probably the hardest way to level because it gets really boring and you don't get as much experience when it comes down to the quest experience.
Tip: I believe that you should never grind unless you have no other options of trying to gain your level. If you have to, I would even recommend instance leveling before you resort to grinding.
Try Not To Get Side Tracked
I remember when I was struggling to get past the lower levels in World of Warcraft, I always got sidetracked and did battlegrounds and professions instead of going to do quests. Unless you are level 70, battlegrounds will not help you . However, it is fine to work on your professions a little bit, but once you reach level 70 (or 80 in WOTLK) it will be much less of a pain to get your professions up to level 375.
Have Fun Playing Wow!
( and remember to do all things in moderation, including World of Warcraft) I don't know why but I just have seen this tip so much its stuck in my head, and I never remember to turn them off in the options menu. :p