If you are just starting out in WoW or are looking for faster ways to level, consider trying a World of Warcraft leveling guide. I've been playing Warcraft since early release. Before that, I was involved in other, pretty hardcore, MMORPGs. As you always want to try on new classes, I advise looking into such a tool like a leveling guide to make sure that the leveling bit gets done quickly.
After seeing a few leveling guides I came to the conclusion that they do help you level faster. Most guides focus on quests as the primary leveling method. That made me curious, is looking better than grinding? In World of Warcraft grinding is a pretty productive method to make some gold. In terms of XP making it also is a pretty efficient method. The downside to grinding is that it requires your character to be well equipped and for the player to know what he is doing. Once reaching the higher levels, levels start to take very hard to get. You'll end up killing in the same spot for a large period of time with little effect.
Questing is the most commonly used method to level up by a World of Warcraft leveling guide. Quests give large amounts of XP upon completion plus the XP received when actually completing them. Besides the fact that they take you in all sorts of places, they are more fun to do and give your character a purpose. The only problem with them is that they can be hard to find and sometimes tricky to do. By balancing these methods from a players point of view, I would say that questing is the winner. Locations and tips on every quest in WoW can be found all over the Internet, the only problem with that is that it takes time. There are some security issues as well if digging to deep on the web. To avoid that, have a look at a leveling guide. Everything you'll need to complete a quest will be at within your grasp without having to waste time looking.
Between grinding and questing, I'd pick questing any day. Grinding can be boring and very demanding, while quests can be done by anyone and there's no need for any expensive gear. The only bad thing about quests can be removed with the help of a leveling guide. Instead of spending endless hours grinding or chasing some quests, consider trying out the only solution to a fast race to the level cap, a World of Warcraft leveling guide.