As soon as they are born, the babies begin their rapid growth. They are pink, hairless, and their skin is translucent enough to see the bones in their skulls, and even a white patch of their mother's milk in their stomachs. The mother will stay with the babies for long periods of time, occasionally coming out to eat and drink. Around day two, pigment begins to develop on dark colored rats (day 3 or 4 for light colored rats), so you can begin to see what the rats will look like. Most mother rats will be fine with you handling the pups, and if so then by all means do it. The more you handle them, the better pets they will make. However, if the mother seems nervous, remove her from the cage or distract her with a treat while handling her babies.
When your babies are about a week old, their hair is long enough to see what colors they will be. Soon their colors really start to emerge. If their skin is dark, they most likely will have darker hair, and if their skin is pink it will be white or light-colored. They will still stay in the nest, as they are blind and deaf and rely on their mother for all that they need. They will paddle around as they learn how to walk, and they may find their way out of the nest. If the mother doesn't notice them, gently replace them back into the nest, or they may get cold and hungry. Continue to handle the babies daily at this point, making sure not to take them away from their mother for too long. Even at this young age they will learn your smell and touch, and will become friendlier, tamer pets because of this early handling.
At around day 13 to 16, your babies' eyes and ears will open. Be very careful at this stage, because they are seeing and hearing everything for the first time and they don't know what to make of it. After a few days, they get used to it and begin exploring their cage. Give them a few safe toys for them to play with, such as a rope, a tunnel, or a safe wheel. Make sure you put the water bottle low enough to that they can reach it, because their mother will start weaning them soon and they have to learn how to drink water on their own. Handling the babies at this stage is even more crucial to their development, as they are most susceptible to socialization training at 2 to 6 weeks.
Often at this stage the babies will be somewhat nippy. This is similar to when a human baby is teething, or a puppy's need to chew. They are simply testing their environment and their ever-growing teeth. You will find them chewing on pretty much anything they can get their paws on, and occasionally they will nip your fingers. If they do this, make a loud 'squeak!' sound and pull away. This should let them know that you are not a chew toy!
After their eyes open, they begin to look and act just like adult rats, though a lot more playful. Keep up the constant handling, which becomes easier at this point because the rats can be away from their mother for longer and longer periods of time. You can set up a play cage for them filled with toys, or take some of the babies out in a safe escape-proof area where they can run around and play with you. Their mother begins to wean them around three weeks, and they are completely weaned by six weeks of age. Around 6 weeks as well, the babies become sexually mature, meaning you have to separate the males from the females including the mother, as they will impregnate their sisters and even their mother if given the chance. Males from the same litter rarely fight, so it's okay for them to share a cage. You can also put the male babies into a cage with other males, though make sure you introduce them carefully, as some males do not take kindly to intrusions of other males, even if the newcomer is a baby. And, of course, a baby can be hurt badly by a large male rat, intentionally or not. The females can be put in their own cage or they can live with their mother for the time being. If you are selling the babies, they are now ready to go into new homes.