A puppy needs his mother's warmth and milk, but at times humans must intervene and provide nutrition to save a pup or litter. While commercial dog formulas are available for the long term, you probably have everything necessary in the kitchen to make a satisfactory meal for your puppy.
Boil the water in a saucepan on the stove, or in a teakettle. Allow it to cool. If you're using goat's milk you can omit this step.
Pour the milk, water (if using), egg yolk, yogurt and corn syrup into a blender. Mix the ingredients thoroughly. Run a spatula around the edges of the blender and through the mixture to release any air bubbles.
Warm the mixture in a saucepan on the stove to approximately 100 degrees; a dog's body temperature is 101 degrees, and the formula should not be cold when the puppy feeds. Stir the mixture to keep it from scalding on the burner.
Place some of the formula substitute into an eyedropper or baby bottle for feeding. The mixture will be somewhat thick; make sure there are enough holes in a bottle nipple for the puppy to easily suckle.
Store any leftover formula substitute in the refrigerator for up to a week before throwing it away.