When I first started Season 5, I was playing with a Holy Paladin partner. Our goal was to run the opposing team out of mana while using our defensive cooldowns to prolong a match. What a switch when playing Mage & Rogue! Most of our fights are over in 60 seconds or less, unless something has gone terribly wrong. This bursty style of play seems to favor quick damage over all else, but in reality it's not about the damage.
Rogues in 2v2 are defined completely by their ability to effectively crowd control one target for long periods of time. Between Sap, Gouge, Kidney Shot, and Blind, our CC capabilities are the best amongst any of the classes. The key to playing any successful Rogue combo is to coordinate CC with your partner, and to execute on those CC opportunities.
Against a traditional DPS and healer combo, there are two approaches to CC. One method is to CC the DPS class, which will allow you easy access to the healer without being "peeled" by the DPS. The alternative is to CC the healer, which gives you the ability to kill the DPS class before they are able to be healed. Which you choose to use depends greatly on the partner you are playing with, along with the enemy composition.
Trying to CC a Death Knight's healer and kill the DK is a mistake in most cases, as the DK will be able to use defensive cooldowns to survive your enslaught. However, if you are able to crowd control a Rogue's healer, they are typically able to be killed in just a few seconds of focus fire. Similarly, it may not be the best approach to try CC'ing a Druid if you have a Mage partner, as the Druid is immune to most of the Mage's CC and will be able to easily trinket out of your Blind (as they are also immune to our Sap in tree form). Knowing who is vulnerable to which of your CCs is a key ingredient in using your cooldowns wisely.
One symptom of a novice Rogue in the arena is the tendency to "tunnel vision" a particular target. This refers to the idea of focusing solely on the target you're DPS'ing, while ignoring your partner as well as your opponent's partner. This will cause you to lose opportunities to CC the enemy or assist your partner, as well as possibly forgetting to watch your own health meter. I suggest playing a few skirmish games for fun, and practicing simply watching the health, mana, and cast bars of both teams. Don't worry too much about your particular target, simply do your best to "watch the field" and see how you do.
A great way to get away from the idea of tunnel vision is to start making use of a few Focus macros. These take advantage of a new "target frame" of sorts. Basically, you choose your Focus target by selecting any NPC/player and typing /focus. This will bring up a new unit frame window for that NPC, which is similar to your target window. You can then write macros that will automatically cast spells on your Focus target, without ever needing to switch from your current target. Here's a sample formula:
/cast [target=focus] Blind
This will automatically Blind whoever is in your Focus target window. I find that Focusing the healer/caster of any given team is the most efficient, as they are typically the class you will find yourself Blinding or Kicking or anything else you choose to bind to a macro. By using these macros, you'll get yourself used to watching two targets at once, and observing the situation with a bird's eye view.
The defining trait of any great Rogue is the ability to make a quick call and a great move with miraculous reaction times. Seeing a healer casting a spell, knowing that the healer's PvP trinket is on cooldown, and knowing that your partner is in a position to assist with a kill of the DPS, and using your Focus macro to Blind the target mid-cast: key plays like these are what set us apart. In order to truly excel in the arena, quick reaction times to CC and interrupt your opponents are vital. There was a time where the mark of Rogue excellence was "kicking a Fel Dom", which was simply a spell with a 0.5s cast time.
Watching your own abilities and actions are not enough in a PvP environment. If you're spending time looking for a button to click (which you shouldn't be) or worrying about which of your abilities are on cooldown, you're wasting time that could be used to monitor your opponents actions. This sort of "full court" observation is the most crucial skill to develop and exploit. Playing a lot of skirmishes and simply observing is a great way to learn these talents.