Whether you are Horde or Alliance, there are a few common ways to level up your character. These will be common factors that you will notice run through every race and faction of the game and leveling for World of Warcraft can be much easier that you might expect.
When a new character is formed, they will immediately be offered a quest or two. As the game is played, a character will be able to hold 25 quests in their log and do 25 daily quests, as well. These daily quests will greatly enhance a players experience points and doing all 25 every day will give the character a great deal of experience quite quickly. The characters that have the big yellow exclamation points above their heads will have the quests for the characters specific class, race and profession.
Killing enemies is also an excellent way to level your character. Massive killing sprees will garner your character many experience points. If you have made sure to keep your character in a home area when you are not playing, you will get rest points, which will make your killing more beneficial. Quests will move your rest points up and will not count against them.
You will be directed to different areas of the world that will have the level of characters you need to kill. Quests will lead you to many places all over the World. These quests will give you more than just the experience, as in gold, silver, copper, weapons, potions and other useful items.
If you are choosing to kill as many enemies as you can to level your character, make sure the enemies are in the red level. These will give you the most experience points. The yellow colored level enemies will give average points, while green is much less. Unless they drop useful items, gray level enemies should be avoided as they will not give any experience points.
Leave your character in a home area when you are not playing to help with leveling for World of Warcraft. You do not need to be able to implement elaborate plans to get your experience as high as possible quickly.