You can either participate in the competition or just watch. If your Dog has a high intelligence, you can have a higher chance of winning.
You can train your own Dog by using the Ball that you bought from Won. The Ball Toss is like a fetch but the ball is the one using. The more you do this, the higher intelligence your Dog will get. Also, using a whistle can be a training too. If you use a Whistle, your Dog will follow you. If he didn't follow you, it means he still lacks of intelligence.
This training is not for the goods of the Race only. This can be use for your farm's sake. If your Dog is trained enough, it will help you drive away a Stray Dog attack.
The Dog Race
Run to the finish line as your dog follows. If your dog stops following, run back toward him until he starts to follow again. You're not allowed to use the whistle or pick your dog up. The first dog to cross the finish line wins.
For winning the Dog Race, the mayor gives you the title of "Top Breeder."