What special care do newborn puppies need?

Most dams will give them the care they need without hesitation. At birth they need to have the birth sac removed, and be rubbed to stimulate them to start breathing on their own and to dry and clean them. If mom doesn’t do this, you may help by rubbing them with a towel. Mom will also chew off the umbilical cord. In rare instances it will continue to bleed and a newborn can bleed out quick, so if you must stop the bleeding, simply dip the cord in a bit of flour to help it clot.
Once the pups are born, they should be seen by a vet and have dew claws removed on the 3rd day.
Provide twice as much food as usual to Mom and have clean fresh water available at all times to help her in her milk production.. I keep my dams on daily vitamins, puppy chow and give them raw beef liver a couple times a week to keep their iron levels up. If they start to look thin, I top dress their food with puppy formula powder to help them.
The first 3 weeks, the dam will spend most of her time taking care of her puppies. She will lick them to stimulate urination and bowel movements and cleans up after them for this time frame.
Check the pups nails and trim them if they are scratching the dam during nursing.
For the pups:
Check on the pups several times a day to see that they are round, nursing, and seem content. Noisy puppies are generally hungry puppies. If they spend a lot of time crying you need to figure out why. Keep the puppy nursery warm, draft free, and dry for the pups’ optimum health. Don’t let a lot of people come in to see them until later as this may make mom nervous which can affect her milk production and how well she cares for her pups. She may also feel the pups are threatened by people she doesn’t know well and become aggressive to protect them. They should be seen by a vet and have dew claws removed on the 3rd day. The umbilical cords should fall off in a matter of days. Puppy eyes are closed at birth, and generally open between 10 and 14 days.
At close to 3 weeks you can offer a bit of puppy chow soaked in puppy formula to make it form a gruel type consistency. Make sure they’re getting plenty of liquid with it so they don’t become dehydrated and develop urinary tract infections while adjusting to the new diet. I worm the pups at 2, 4, 6, and 8 weeks with a liquid wormer I buy from my vet. Parasites can be devastating to a pups health, so it’s money well spent.
I strongly believe they should be allowed to nurse until their dam decides to wean them. I’ve had many pups still sneaking occasional snacks off mom at 7 weeks of age. It’s easier on her and the pups if this process is as gradual as possible. This is just one of several reasons why my pups don’t leave Mom until they’re 8 weeks old.