If you need to take puppy-feeding into your own hands, you have to be careful about what you give your pup. There are different types of milk on the market, and the cow's milk you pour on your cereal isn't the same milk you should give a puppy -- they can't digest it properly. While formula is arguably the best solution, soy milk is also something you can try, as many dogs find it agreeable to their digestion while satisfying their need for a liquid diet.
Take your puppy to the vet before starting any type of diet. Some dogs can't tolerate soy, or are allergic, and shouldn't have products containing this ingredient. Your vet can help you determine if it's safe for your puppy as well as tell you how much the dog should have.
Remove your soy milk from the fridge and let it rise to room temperature. A mother's milk would be warm, too, so your pup shouldn't be drinking cold milk the way you would.
Fill your puppy-nursing bottle with a few ounces of soy milk and, with your pup laying on his stomach like he would when feeding at his mother's side, insert the nipple of the bottle into his mouth. If he doesn't suck instinctively, give the bottle a slight squeeze to squirt out some soy milk, which will prompt him to suckle.
Allow your pup to suckle according to your vet's instructions. The amount that he should consume is based on his size, breed and age -- only your vet can make that distinction until you're experienced. Puppies should have several small feedings over the course of a day rather than one or two larger feedings, so you may have to feed him every few hours.
Disinfect the bottle and nipple after each feeding by soaking it in boiling water for 10 minutes.