I can never wrap my head around the fact that barrels and poles are strictly western disciplines over there... It seems so crazy to me! I can't imagine running poles on my little arab in a weastern saddle. On him, I crouch over his neck and squeeze in as tight as I can, because he goes with a hair breadth of the poles! I couldn't do that in a western saddle.
Now, I NEVER had a trainer and I don't think you could even find a trainer who specializes in gaming in my city. Mostly, it's practise practise practise! Also, don't try to go fast until you have the patterns absolutely perfect.
You should make sure your horse can collect and extend, move off your leg at a walk/trot/canter, have good turning aids (body follows his nose/no shoulder popping out/bum swinging out). You should also be able to move his shoulder and his bum seperately, even just from a halt. Should have good canter leads established, and flying changes will help a lot, but most horse once they have the pattern down will put in their own changes.
The biggest thing to master in gaming is your pockets... On all turns the theory is to come into the turn wide and come out tight. This puts you ona direct line for your next obstacle, wether it be the next barrel or the line of poles on the way home. It takes much less time than if you go into your turn tight and your horse balloons out exiting the turn. It slwos them down, throws off your line.
Never let your horse get fizzy on the start line, that's a big thing! Always work on calm calm calm. I like to do a lot of turns... I will walk into my turn wide, stop about halfway around, leg yeild him away from the barrel/pole a few steps, then come in tight and continue the track out of the turn. This excercize helps a lot with horse who tend to drop their shoulder in on the barrel/pole. Once they get it down pat I will do it at a trot.
Also, don't limit yourself! There are tons of different games out there that will sharpen your horse turning, get him listening to you, and prevenmt him from getting stuck in one pattern or bored. Look up games such as clover leaf or running tee for good poles practise, You can use straight barrels or the stockhorse race for barrels practise. There are also many unrelated games that nonetheless are great for turning, sharpening of aids and boredom. Soem great ones are bonfields bounce (poles and jumping), Scudahoe (poles, barrels and jumping), Flagging, and many more. Flagging is a huge one here in Aus, almost bigger than barrels.
Let me know if you want any more info on anything i've said!
Most of all, just have fun! Don't get mad at your horse if ti takes him a while. It took me about 3 years on my arab, and now he has been our zone champion gamer 5 years in a row. You'll get there!