You start off with a young duck that doesn't really have experience in racing and it needs to be trained. You can simply do this by tapping your duck. Each time you tap it, you get experience points and when you have enough points, you level up.
When you feel like your duck is strong enough, you start a race. Tap as fast and as many times as you can to win the race. When you win a race, you get money. Use this money to buy trainers and/or to buy items.
After winning enough races, you may try to compete in a tournament. These consist of a couple of races and the winner takes it all! You can win a lot more money here, but competing also costs money.