Here are some common acronyms you will most likely encounter in game, and on this site :)
LFG = Looking for Group, means that you are looking for a group of people to play with either to finish a quest, go to an instance, go on a raid or something of that sort.
ex: LFG to finish a quest
LFM = Looking for Member, it basically means the same thing as LFG but the other way around, you are in a group and looking for more people to join.
ex: LFM to go raid some town
LFxM = Stands for the same thing as LFM except for x stands for a number, it is used when you are looking for more than one member.
ex: LF3M to come help me with a quest
FP = Flight Path or Flight Plan, a flight path is where you can fly from one town/city to another
ex: I am going to go to the FP
AFK = Away From Keyboard, you use that when you are not at the keyboard
ex: I was AFK
COD = Cash On Delivery, when you mail someone something and want them to pay you for it before they get you can use this.
ex: I will COD it to you
DE = Dis Enchanting, something enchanters do to items to get things to do enchants
ex: Will you DE this for me
G2G or GTG = Got To Go, when you have to go and leave the game you can use this
ex: I g2g will be back later
NPC = Non Playable Character, that is a character in the game that isn't human..it is played by the computer
ex: That is a NPC
WTS = Wanting To Sell, this is usually in the trade channel and you use it if you want to sell something
ex: WTS Copper bar
WTB = Wanting To Buy, just the opposite of WTS..use it if you are looking to buy something
ex: WTB Silver bar
PST = Please Send Tell, it basically means to whisper the person..a tell is like a whisper or private message.
ex: If you are looking to join my group pst
AH = Auction House, the place where you buy and sell stuff
ex: Go look in the AH
BRB = Be Right Back, this is used when you are going to be away from the game for a little bit but still in the game.
ex: I will BRB, need to go and get a drink
DPS = Damage Per Second, you use this when talking about weapons
ex: What kind of DPS does that have?
GM = Game Master, someone that helps make sure the game goes smoothly and can assist you if you need help or have a problem
ex: Just go to ask the GM
Now here are the abbreviations for some of the places in WoW. You will use these a lot and it will save you a lot of time and typing so these are good to know.
UC = Undercity
Org. = Orgrimmar
TB = Thunder Bluff
Xroads or XR = Crossroads
SM = Scarlet Monastery
BFD = BlackFathom Deeps
BRD = BlackRock Depths
IF = IronForge
RFD = RazonFen Downs
RFK = RazonFen Kraul
WSG = WarSong Gulch