Well first let me say welcome to WoW! You are about to begin a long journey through a very complex game. 
     There are several main aspects of World of Warcraft that I'll break down for you. 
     Ultimately, the greatest aspect of this game is gaining levels and experience through killing monsters and completing quests. Where your quest can make all the difference between a good time and a bad time. 
    The second biggest aspect of WoW is the massive community within the game. There are over 8.5 MILLION players to this game now, and at any given time there will be several hundred people online in one world at any given time. Much like any real life community, there is an ettiquite to WoW and engaging with other players in the world. 
     Now, I know lots of you are thinking ok, but what about KILLING other people, which is where the PvP system comes in. Now I wouldn't recommend PvP for newbies untill you've got most minor aspects of the game figured out. (note that a newby is someone who is new to a game and wants to learn. A NOOB, is someone who refuses to be corrected when they do something wrong, even when others who are much more experienced are trying to kindly point out that there is a better way to do something.) 
   But the PvP system is designed to award points for every player you kill that are close to your level, you can spend these points as well as tokens you earn from completing a battleground (a encolsed area where a team of alliance and horde enter for match of capture the flag or king of the kill or "beat the enemy's leader" match.) 
     Another big aspect of the game is proffesions. You can train two main proffesions, and any amount of secondary proffesions. Basically a proffesion is something like leatherworking, blacksmithing, mining, skinning, alchemy etc that allows you to create and find items you can use or sell from things found within the world. 
   Alright, Now that you've got a grasp of the main focuses of World of warcraft (keep in mind that there is more to WoW than I've listed here, but I don't want to spoil the discovery ;). Hopefully this will be enough to get you a foothold. I'm about to go into more detail, so the people that really want a good start in WoW, keep reading, if not, go nuts and explore, its fun!

The Community and Etiquitte
    There are many of those in world of warcraft who belive that it's ok to run up and take a chest you just cleared all the mobs away from, but let's face it, they ruin the game for a cheap laugh for themselves. 
    Basic courtesy dictates that you ask someone if they would like to join your group to help kill something. But instead what you get is people whispering you saying "Heal mara for us" (mara is an instance, one of those neat things you get to discover on your own). Also, never, EVER run up and take something without asking someone. (mining allows you to get metal ores from little deposits that appear once in a while out in the world, and lots of people will run up and mine it while you kill something beside it (you cant mine and fight at the same time) then say "oh sorry i thought you we're just killing this mob in the middle of no where for no reason at all" and run off with your ore.
    Basically, Don't do anything to anyone else you wouldn't like dont to yourself, it's a cliche, but believe me, bad reputations build fast, and they can completely ruin a character unles you want to pay for it to be transferred to another server.

Proffesions
    Time to choose your job. Proffesions in WoW are tradeskills, allowing you to fabricate items ranging from cloth armor to plate armor to guns to mechanical chickens to potions to... well.. just about anything you could possibly need. heres the basic rundown

Gathering Proffesions
Herbalism - allows you to track plants on your minimap and harvest them
Skinning - allows you to use a skinning knife to collect leather from fallen beasts
Mining - allows you to use a mining pick to dig up ores found in deposits, deposits appear on the minimap

Manufacturing Proffesions
Alchemy - Allows you to turn herbs found from herbalism into potions that provide temporary bonuses to stats or regenerate health and mana. (useful for any class really, never a bad choice)
Blacksmithing - Allows you to turn metal from mining into armor, weapons and a few other things
Engineering - Allows you to turn metal from mining into gadgets, bombs and guns, as well as dozens of other neat little things
Leatherworking - allows you to turn leather from skinning into armor and a few other things
Jewelcrafting - allows you to turn gems and metals found from mining into rings, amulets, trinkets and various other items
Tailoring - Allows you to turn cloth found in the world into cloth armor and a few other things
You can train two of any of the above skills, And there are two ways to do so
For money: go with two gathering proffesions, you can sell the materials on the auction house to people who need them for their own proffesions for quite a bit of gold
For yourself: go with a gathering and a manufacturing that go with eachother and will work for you (don't choose tailoring if your a warrior, the cloth armor isn't going to help. and stick to something like skinning/leatherworking so you can gather your own materials)

Most proffesions will require some kind of item that must be in your inventory to be able to perform the proffesion (you have to have a blacksmiths hammer in your backpack as well as be present at a forge/anvil in order to actually make something using blacksmithing.

PVP!
Ok, so you've got your foothold, you've got a character that has some greens, a decent spec (you think) and a good weapon. Head to the nearest capital city and ask a guard for the Battlemaster. Run your but up to the little flag on your map and que in for whatever is your level and you feel like doing. Heres the basic rundown of the battlegrounds

Warsong Gulch
10 Vs 10
goal: capture the flag 3 times to win
size: roughly the size of your level 1-6 zones.
Level req: level 10 or over.

(also keep in mind that you wont be facing level 60's at level 10 in a bg (battleground), there are brackets for 10-19, 20-29,30-39 and so on up to level 70. Although if you are in the lower half of your bracket you will be getting killed alot)

Arathi Basin
15 Vs 15
Goal: There are 5 areas that your team can hold. You must click on the flag at each area to capture it, once captured, that area will start awarding you points. For each point you have captured, the faster your points go up. Right click an enemys flag to capture it.
Size: A little under twice as big as warsong Gulch.
Level Req: 20 or over

Alterac Valley
40 vs 40 *matches can be anywhere from 20 vs 20 to 40 vs 40, depending on the amount of people that want to join.
goal: Kill the enemy NPC, deep within the enemys base. This also combines a slight arathi basin strategy, with areas you can capture that spawn npc guards to defend your base, the more areas you capture, the less guards, the easier it is to get to the Final boss.
Size: a but smaller than durotar (orc start zone)
level req: 50 or over

For every battleground you win, you are awarded three marks of honor for that battleground which will appear in your inventory and for every loss, you get one. (wsg gives you warsong gulch marks of honor, ab is arathi basin marks of honor etc). You can combine these with the honor you get from killing an enemy player (must be a real person, not mpc) to buy things near the battlegrounds portal entrances, or in your citys PvP rewards building. These rewards range from level 18-70 and are good quality. (weapons, armor, potions and other goodies) You are also rewarded honor points for killing enemy players out in the wilderness too, so dont be afraid to attack that alliance as he's bandaging up.