World of Warcraft has been previously explained in this post located here. I gave a quick overview of the game and the genre. Now, a little about the game. Most of this discussion will revolve around game play since the Burning Crusaded Expansion.
Leveling means increasing your characters level, which allows you access to more powerful skills, abilities, and sometimes forms. Your character begins at level 1, in what is known as a starting zone. Each race has their own, sometimes shared with others( trolls and orcs, and gnomes and dwarfs share one, while the other races have their own). Your first quest giver is standing right in front of you, with a big yellow exclamation mark over their head. Quest in warcraft can usually be completed solo, and once a quest is completer, the quest giver has a yellow question mark over their head, and will reward you with experience, money, and sometimes items.
The max level in Warcraft is currently set at 70, and it can take anywhere from 5 days playing time and up to reach that level. Those that have leveled to 70 before, usually can do it faster by knowing where to go, which quest to take when, and where and when to just grind to gain experience.
You gain experience from killing mobs around your level, completing quest, and discovering new zones. The experience you gain increases as your level increases, but also the amount of experience needed to level increases. At level 1 I believe it is 1000xp to level, compared to level 70, which requires you to gain over 700,000 exp at level 69 to reach.
Talents and Specs
All classes, have three "talent trees" that further defines their class. Beginning at level 10, you receive 1 talent point per level gained. You then spend these talent points in your specific trees. For example, a warrior has an Arms, Fury, and Protection Tree. Arms has useful talents to augment the other two trees, but also is commonly recognized as the warrior PVP( player vs player) tree. Fury is for Pve DPS, and Protection is where warrior tanking skills are. It is not recommended to level as a protection spec, because there is little to no dps talents in this tree.
Based on your talent choices( and there are plently of options listed on the official WoW class forums) you can specialize in other skills. A mage can focus on frost, fire, or arcane magic, or a combination. A druid can become caster dps, a healer, or a tank/dps class. Even priest, who are usually just known as pure healers, have a dps tree, which at end game is very, very formidable.
This is where Warcraft, in my opinion, flounders a bit. A player can level all the way to 70, doing quest alone, never entering an instance. At level 70, you have two choices, raid or PvP. Blizzard recently added some repeatable daily quest, which you can do 10 of a day, which nets you about 120g for around 1.5 hours worth of time. Raiding requires time and dedication, money for repairs, consumables, etc. PvP requires time, dedication, but not the money sinks that PvE has. Blizzard has made PvP reward gear very comparable to Raiding gear, which allows those that love PvP the ability to have gear equal, or in some cases, greater then current raid gear.
In conclusion, warcraft is a solid game, highly addictive, but also a huge time sink. You will spend your time farming for money, materials, reputation items, and gear. Just so you can get more gear from harder instances. Currently, the best MMORPG on the market, and the one with the largest fan base. It will be interesting to see how it holds up against the upcoming Conan and World of Warhammer games.