General Arena Guide
As a rule of the thumb, you should always be seeking out gear that improves Resilience and Stamina the most, if you need some pointers just look at your class's Arena and PvP armor, which you will be wanting to get eventually. What Resilience does at higher amounts is simply mitigate the chance of being critically struck, and when you are, you will take less damage from blows.
Why is this important, you may be wondering. Arena weapons (and PvE weaponry) have obscenely high DPS! if you receive a critical strike head-on, it's not uncommon to see yourself one or two-shotted. It happened to everyone when Ragnaros's Hammer was first used in battlegrounds and when Ashkandis became popular to use within PvP areas. People would drop quickly without knowing what hit them. Now, with resilience, we're able to level the playing field and have a decent chance at out-maneuvering people with huge, hulking weaponry.
An "ideal" level of resilience is over 300, but you shouldn't stop there, the more you have, the better you'll be since you will be surviving a lot more hits from your enemies, giving you the extra seconds you need to deal with them!
Coupled with Resilience, Stamina should be your next concern, and for this there's no real limit, get as much as you can, and get it as soon as possible, a few Hitpoints may mean life or death within the arena, especially against rogues and burst teams.
You must also always wear your Insignia of the Alliance or Horde to a match, it's a free 2 minute cooldown dispel (if you bought the best one) that removes all effects that could harm you; if you use this early on during the battle you might be able to use it again at a critical moment and turn the match over to your side.
Try to wear a burst damage trinket in your second slot, the ones that say "Increases your attack (or spell damage) by ___ over 10 or 15 seconds", these trinkets will let you open up with more damage and possibly boost you once more during the battle. While the damage may not seem that noticeable, if you score a critical strike on the enemy while the buff is ongoing it'll be that much devastating!
Stay calm! nervousness and/or overconfidence will net your opponents some starter points - be confident in your abilities and face whoever comes at you head on! they're players just like yourself, so there's no reason to get nervous nor overly excited to the point you forget your abilities!
Always keep an eye out for the opponent's tactic - are they both going to attack? who's playing support? figure this out quickly and attack the weakest contender, once you take them out, you can start moving on to the strongest one.
Don't attack warriors if they have a healer with them! kill the healer first. This is very important since if you go all out on the warrior, the moment you fail on killing him with any heals he obtains he will become twice as deadly with all the rage you fed him. Try to ignore them or crowd control them as soon as possible.