As mentioned, going to a show is best. A field day is the best show to go to for those who want to learn what to look for in quality. You have a more hands on experience at field days and the judges will explain why they chose which chinchilla for which placing and compare for you the differences between chinchillas they are judging.
If you are unable to make a field day, you can also learn by visiting judges or graders and having them show you under show lights, what to look for in qualities. Fur strength and resiliency are extremely important as well as other traits mentioned previously in this thread.
For someone who does not know what to look for, an easy way of finding out fur strength and resiliency is to blow on your chinchilla's fur. If it bounces back quick and stands up straight, that is what you want.
If it lays down or does not bounce back completely, it would show weakness of the fur. If you want to learn more about density, using two fingers, you can squish together the fur, and it should be thick and plush between your fingers. The thicker the fur is, the denser is it. Fur that is wavy/weak, lays down, thin, or cottony in appearance, and off color, are all traits you don't want to breed for among others.
Basically, when you look down at your chinchilla's fur coat, you want it to look like millions of tiny needles are staring back up at you.
Conformation is equally as important to other traits mentioned. Chinchillas that are well rounded, with thick necks, not wedgy in appearance, are what you look for when you look at conformation.
Clarity is a trait that is easily lost and harder to maintain because it is recessive. Size is perhaps the easiest of traits to breed.
Putting two top show chinchillas together will not always guarantee you great offspring. Try to pair animals that compliment one another, and one that may improve what the other lacks in quality is what you want to further improve upon what you produce in your herd.