There are a couple of things I look for. I want a trainer who follows the system I use, teaches current training methods, is skilled themselves, and is a great teacher. I don't want necessarily the nice teacher. I want someone who will pick apart what I'm doing and give it to me straight. I learn nothing from 'that's great! keep doing that!'. If I don't know I'm doing something wrong, or not doing it the most efficient way I can't fix it. The only way I can grow is for someone to tell me. And at this point in my agility career with the most advanced dogs, it really takes someone with a good, critical eye to continue helping me to grow.
I think it is also important that the trainer be competing in the venues I am interested in. Someone who trials in USDAA and AKC (or UKI, but we don't have it around here) is much more useful to me than someone who's main venues are NADAC, CPE, UKC, and TDAA. There are differences between the venues, and typically different levels of competitiveness. I want a trainer who is competitive in their chosen venue, and it doesn't always transfer. Someone who is competitive in UKC for instance may not be nearly as competitive in USDAA. There are just different things required, and a competitive team in a smaller venue where there are fewer fast, competitive, skilled teams more than likely isn't going to be competitive in USDAA or AKC. The person I train with should have proven the way they train can be applied successfully, and that they can train a dog to the highest level. A good example is NADAC around here. The people competing in it aren't competitive in masters in AKC. They lack skill and often speed. So despite them winning in NADAC they are unable to in AKC.
That includes speed. I'm a little more leery of going to someone with slow dogs. It makes me wonder what they are doing to create it. Are they demotivating? Do they not know how to get the best from the dog? A moderately fast dog (especially when not a BC) is typically (though not always) a dog someone has worked hard on to get that much speed from it. They know the tricks of the trade to get the most from the dog.
I want someone who can help me meet my goals, which are admittedly big goals. It's why I have to go outside of my area for a trainer. It's either 3 hours away to someone in TN, or online with Silvia Trkman. There aren't any trainers in my area who can help me to progress further than I already am in my area.