here's one very simple recipe:
take one whole chicken and remove the giblets*. put the chicken breast-down into a large pot and cover with water. add spices to taste, i use about 1 tablespoon of dried thyme, oregano, basil and parsley, a teaspoon of dried or fresh rosemary and a clove of garlic, crushed. cover and gently cook on medium heat until the bones of the wings pull out easily, usually about an hour and a half.
* if you aren't planning on feeding any of this to any human members of the family, you can cook the giblets along with the chicken.
remove the chicken from the pot and add cut up vegetables to the soup, let simmer while you debone the chicken. i usually use carrots and peas but sometimes also celery, leek, broccoli etc.
debone the chicken and separate the "good" meat and the bones, skin and cartilage. pull the meat into bite-sized chunks and add back to the soup. add a little salt if you want.
that's it for the main recipe, you can serve it as a meal for humans or use it as a kibble topping. you can also add some pasta or rice to make a more filling meal.
one thing you need to be aware of is that in this cooking process a lot of collagen is extracted, so if you refrigerate this soup, it will turn into jelly. don't be alarmed, this is absolutely natural and a very healthy food. it will become liquid again when you warm it up.
if you use this just as a "kibble topping" (e.g. a couple tablespoons per meal), there's no need to use a calcium supplement if you are adding it to a comemrcial dry food. if you want to feed it as a replacement meal (e.g. with some cooked rice, pasta or potatoes), you'd want to add about half a teaspoon of egg shell powder (or 900 mg of a calcium supplement) to balance out the phosphorus content.
if you have a crock pot, you can cook the entire chicken until the bones turn to mush (e.g. you'll be able to easily break down even the thigh bones with a spoon). in that case there's no need for a calcium supplement.
disclaimer: this is not a recipe for a complete dog food. it won't hurt to feed your dog this for a week or two at a time, but the nutrient levels are not designed to meet all of the dog's needs long-term.