My dog just had puppies a week ago. There's one sick puppy. She hasn't been active and won't latch on to feeding. I bought Karo syrup and puppy milk as advised by a friend but I don't know how much I should give her, or how often.

A puppy that young should be fed every 2-3 hours.
Is mom cleaning and letting her snuggle with the rest of the litter?
If not you will have to stimulate her to pee and poop and also keep her warm.
The Karo syrup will come in handy if she becomes weak or listless between feeding, just a little rubbed on the gums and tongue will be fine. And then feed her immediately.
The feeding instructions for the puppies weight should be on the packeage follow them closely not all puppies are the same she may drink a little more she may drink a little less.