The first step is learning the colors, patterns, and the genetic codes behind them. You'll learn what colors "go together" to create other colors and so on. This part honestly takes the longest as some of the genes are tricky!
That's not all though.
You'll need to consider the shape of the hamster's head shape, ear placement, size and weight (the bigger the better), body shape, and so on. The NHC has good guidelines for type.
Once you're more familiar with the genetics and the physical appearance of a nice hamster, you'll need to think about selection. If you're breeding Longhair hamsters, you'll want to select for the longest coats. If you want the darkest Sable, you'll want to select hamsters with very strong Umbrous. Want a really nice banded hamster? You'll want to select away from hamsters with color faults. A really nice Golden? Choose ones with the most defined cheekflashes and crescents.
All of these traits are controlled by polygenes. We have polygenes too, for example, there's multiple shades of brown eyes and brown hair! It takes some time to lock in the traits you want.
For breeders, the age of the mother is very important. You run more risk of losing pups, the mother, or both the older she is. At the same time, you don't want to breed the females too early!
First time mothers do sometimes eat pups. Just because they've had a litter doesn't necessarily mean all will survive. She'll still cull pups if they're sickly or malformed. Plus, some mothers are easily excited, others aren't. Some go crazy trying to put pups back in the nest! Others just let them wander.