Their are two main approaches to leveling up your character in World of Warcraft.
The first approach is grinding while the second approach is questing.

Grinding

The term grinding means a player, such as you, fights mobs or creatures over and over with no quest behind it. Both pros and cons are found when you play the game this way. As you kill the mobs over and over, you will gain junk items as well as a chance of a great item. You will also gain copper/silver/gold and experience. However, their are also the cons. Grinding is not for every class, nor is it for every person.
When a player grinds, it is repetitive, boring and causes you to lose interest in the game.

As opposed to:

Questing

In World of Warcraft, the Non-playable Characters (NPC's) give the player quests.
These quests will often tell you to collect items, defeat creatures, or find something.
Questing has its pros and cons as well as grinding.
Once you complete a quest, you get a massive bonus of experience, almost always a copper/silver/gold reward
and often times a decent item for your level. Depending on the level of the quest and its difficulty, sometimes that
item is rare (blue). Questing is also a good choice to level since many quests link together and you don't even know
but your getting two done at the same time.
The con however, is spending time lost looking for the location of the mob you need, or the item you have to find and collect.
The downtime when you’re lost can add up and seem like an eternity.

Overall, it is said that grinding from 1-70 takes 3-4 days of played time longer than someone who is simply questing. It is up to the player, kill mobs repeatedly with no player interaction, or complete quests with friends, get items and gold and have a goal.