Chuinshao summed up the dogs fight very well and I use macros similar to what Typan uses. There's also an addon at Curse called StoneGuardTauntCues that tells you which dog to pull when (and will negate the rest of my post).
One thing I've found helps me for that first fight that's rather unconventional: after the first detonation, treat it like a new hand in blackjack every time a dog detonates. I learned this before discovering that add-on, and still like my way better.
In blackjack, your choices when dealt a hand are to Hit or Stay. In this fight, your choices are to Taunt a dog over (Hit You), Keep what you have (Stay), Co-Tank Taunts off you (Hit Co-Tank).
After every detonation and a new dog starts petrifying, decide if you want to Hit You, Hit Co-Tank or Stay. My rules are:
- If I have two dogs and one is petrifying: Stay
- If I have two dogs and the one my Co-Tank has is petrifying: Hit Co-Tank (with the dog that has the lowest energy)
- If I have one dog and it is petrifying: Hit You (with the dog on the Co-Tank with the lowest energy)
- If I have one dog and it isn't petrifying: Stay
Make that quick evaluation everytime a new dog starts petrifying, and tell your Co-Tank. That will get you through 90% of the situations. Make sure you follow what Chuin said on the swap the first time at 40 energy, since that is essential for this to work properly.