When I first got Polaris she was only five weeks old and very sick. I had to feed her with a syringe, and it was touch and go for a while.
My advice from what I learned:
Give the puppy nearly constant contact. Hold and carry him frequently through the day, giving him lots of affection and soothing sounds. Puppies, just like human infants, do much better if they’re held next to a beating heart and have someone giving them affection. While you’re watching TV, lay him on your chest, for example, and you might want to make a sling to hold him near you while your’re doing chores and the like. I’m not saying it has to be constant, but the more contact, the better. There is a dog toy out there which plays a recording of a heartbeat and you put a warm water bottle in it which some people have said is very comforting for very young pups.
Put his sleeping crate/box right next to your bed. I’ll let others share the frequency of feedings and the like, but you’re most likely going to have to get up with him during the night. Often, puppies are very frightened if they’re all alone, and even just putting your hand down into the box with him is comforting.
Watch his eating habits. Dogs most frequently show the first signs of sickness by refusing to eat. A tiny puppy can’t go long without food and water before feeling the effects of it (some will even faint if their sugar levels get too low).
Don’t give him any baths yet. Wait until he’s at least five or six weeks for that. Until then, wipe his fur with a warm, wet towel if he needs it.
Try to give him as many new exposures as you can, as long as he’s healthy. He’s going to have a lot of issues as he grows up, because he hasn’t been properly socialized with his brothers and sisters. You’re going to have to teach him bite inhibition, for example, since he won’t learn it as he usually would.
As soon as he’s vaccinated, get him playtime with other (healthy) puppies. He’ll need it to learn “dog ettiquette” and the requisite canine social skills. Now, he’ll probably always be a bit shy or possibly aggressive towards other dogs (depending on his temperment) but the younger you can get him socialized, the better. Until then, have him meet a lot of friendly people. Introduce him to the world around you, different smells and the Evil Vaccum Cleaner Monster.