TThis is from the perspective of having a ret pally as a partner, but a lot of this probably applies to any combo with an SL/SL lock. This way of playing may change a bit come the next patch, with people possibly trying out Haunt, but SL/SL will still most likely be very viable. For lots of great information on arena as a Warlock check out Megs at http://outofmana.blogspot.com/
First thing is first. Prep before the arena starts. While in the starting area, you will be very busy. First, summon a healthstone and trade with your arena partner. While you are trading, beging summoning your pet. You can summon your Imp, give both of you fire shield, then summon your Felhound. Make sure you put up Fel Armor as well as Soul Link. Make yourself a cookie as well. Then cast detect lesser invisibility and underwater breath on both of you. The invisibility buff helps with Mages, and the underwater breath is just more crap that has to be dispelled/eaten.
Make sure you take your Felhunter's silence off of auto cast. Auto-cast is for the 1300 bracket. You may get lucky sometimes, but you lose alot of the importance of your pet.
When the arena starts, depending on the team, you may be the utility (like my Warlock/Paladin combo. I do damage nice and slow while the Ret Pally blasts opponents to bits.
Be smart with your abilities. Death Coil is one of the abilities that Locks really like to misuse. Do not use it as an oppener. It is better used as an OH SHIT button later, or even as an interrupt at the last second. Depending on your opponent, you will use different strategies.
Paladin: There are different methods for Ret and Holy Paladins. You should DoT up a ret paladin and do your best to stay away from him. Once he bubbles, he will be easy pickins. Ret Paladins dont usually bother with cleansing themselves of your dots which is very convenient. Holy Paladins are a whole different animal. They will often times cleanse your DoTs, which means that Corruption and Siphon Life go bye bye. Instead of using Curse of Agony, you should keep curse of tongues on his as all times. Since every Pally heals besides Holy Shock has a cast time, this gimps them severely. While your partner pounds away at the Paladin's partner, you should keep him feared, and silenced whenever you can. This will generally force him to blow his bubble without even taking any damage. Once his bubble is up, you should switch to the pally and burn him down. Most often see them with: Ret with a Resto Shaman, Holy with a MS Warrior or Warlock.
Druid: Druids are a tricky animal, but hey can also be blasted down possibly faster than any class if done right. They key is to find the Druid in stealth kitty form. You DoT everything in sight and got to work on the Druid. A nice fear, silence, death could, fear combo is very handy right here. If you dont give them a chance to heal, they arent very good to anybody. I have had several matches where the Druid got burned so fast that they didnt even get a heal off. If you can burn them down super quick, at least you get them to use Nature's Switftness. You should treat Boomkin Druids in much the same way. Boomkins have cast times on many of their spells which makes the silence that much more effective. You probably arent going to see Ferlol Druids in 2v2 above the 1500 brackets. Most Often see them with: MS Warriors, Warlocks, Rogues. Boomkin can be found sometimes with Mages.
Warriors: Warriors can be very easy or very difficult depending on their skill level. You basically want to DoT them up and line of sight them so that they can intercept you. Warriors also have alot few anti-fear abilities that makes it hard to keep them off of you. Curse of Exaustion can be good option if you have it. Play keep away as much as possible, and use your CC on their partner to put the pressure on. Most Often See them with: Resto Shaman, Resto Druid.
Rogues: I hate Rogues so much that I am leveling one. They have Cloak of Shadows and Evasion, which can give pretty much every class fits. They also have a number of stuns which can take you out of the fight. If you get the drop on them (if you have perception and find them), DoT them as quickly as possible and run away. This makes it so that they cant Sap you. If their partner is another Rogue, try to get him dotted up as well. This will make them blow their cloak of shadows before they are ready.....or else they will be at less than half health when your DoTs are done. When they blow cloak of shadows, run far away. It wont last long, but if they stunlock you it wont matter. When it is up, reapply dots. You should save your trinket for either a 5 point kidney shot or a blind if they are focusing on your partner. I used to think Rogues were unbeatable, but they are very beatable with the right strategy. If they are using a Priest as a partner, it is that much harder. Most Often See them with: Rogue, Discipline Priest, Resto Druid, Frost Mage.
Priest: Perhaps the most squishy class in PvE, they are also one of the most difficult to kill in PVP (at least as discipline). They can heal, mana burn, and sheild. One decent method is to DoT and CC them while you focus on their partner. If they waste their Pain Supression on their partner, do the Ole Switcharoo and blast the Priest to bits. Make sure to try and fear him first chance you get to burn his fear ward. After that, it becomes a bit easier if you time it right. Be careful not to ignore them as they can burn off all of your mana in a hurry. Shadowpriests are another story. Just DoT them, then fear and silence when you can. They are especially hard to drop like a Discipline Priest is, but can do ridiculous amount of damage if you dont kill them. Most often see them with: Rogue and Hunter.
Hunter: I have not seen a Hunter in weeks while doing arenas. They arent represented in higher brackets, but they can be a royal pain if you meet them (especially if they are running with a Discipline Priest in a drain team). Hunter strategy is pretty straightforward. DoT them and their Pet and run away. If they are on a drain team, they will be using the ridiculous Viper Sting on you. You may find yourself wondering where you mana is very quickly. Dont get out in the open against a Hunter if you can help it. They can do a large amount of damage, but not so much if they can see you. They usually have to be standing still a well. You could see all three specs of Hunter in Arena, though I think that MM is the most popular. If a Hunter is BM, kill his pet. This is easy to figure out when his pet becomes big and red. They will both be doing increased damage, so to slug it out is suicide. LoS and drain the pet while he beats on you. If you kill their pet, they have been effectively gimped. Most often see them with: Discipline Priest and Resto Druid.
Shaman: The Shaman is often the first focused on. I rarely see any Shaman who arent Resto. I have seen a few Enhancement Shaman but they go do quickly. The Shaman is very easily crowd controlled, but you need to stop them from Ghost Wolfing around pillars. Most of their spells have cast times, so they are very easily silenced. Another good idea is to kill the totems. There is a macro that makes your pet go and kill the totems. Windfury can be dangerous if coupled with a Ret Pally or a MS Warrior. Take down the totems and take away any advantage they have. Most often seen with MS Warriors.
Mage: The mage is a royal pain to melee classes, but can be handled fairly easily as a warlock. Get your DoTs off on them and LoS. They will eventually have to Ice Block. Reapply DoTs. If they get into your LoS, fear them. Watch out for counterspell. If they use it on you shadow spells, either run away or use immolate and then run away. Save silences for when they try to Polymorph or use a shatter combo on you. You can banish their Elementals, but I recommend just killing them. They have a very low number of hit points. Most often seen with Mages and Rogues.
Warlock: The mirror of yourself. Against a Warlock, just do what you do. Make sure to keep your Shadow Ward up whenever possible and keep them dotted. Fear and drain them whenever you get the chance. This will come down to who is the most skilled. Most often seen with Druids and Shadow Priests.