I recommend finding someone who has produced safe, sane, and successful games horses and enlist their help and advice on-site. Training for any discipline well involves a lot more than just getting on and practicing what the finished product is. There's foundation to be laid, and if that's gotten wrong, then there's a lot of tough fixing to do.
Find a trainer, or at the very least an experienced games rider who has brought a greenie along and understands and is able to accomplish the task properly.
You train a curly the same way you train any horse though.
A game horse should be sound both in mind and body. Easilly stressed out horses don't normally fair well in games and tend to get hot and sour easilly.
I recommend a good reining or dressage trainer before you get to the games to get them a really sound foundation.
They should w/t/c using their bodies effectivly. Be balanced and relaxed.
You should be able to move their body parts independently and they should move laterally as well as forward.
They should have good legs. Do you have any conformation photos of your horse?
They should stop every time you ask as well as back. There are some good threads here on barrel racing which are helpful for all gamers.
What types of games are you doing? Are you riding english or western? What is YOUR riding experience?