Chicken soup is so simple and basic you don't need a recipe to make it right. There are just a few things beyond the name you need to know.
Basically, you have to boil chicken until it's done, remove bones and add salt, spices and some sort of pasta. Here come details and variations.
I always skin the chicken before boiling. It makes clearer and leaner broth. Nobody likes to dive through a scolding hot layer of fat to get to his soup. For that matter, a lean chicken is better than a fatty one. If you find it ridiculous to pay two times more for a free-range chicken, trim the fat mercilessly. Sometimes I cook two chicken at once: fried chicken legs make one dish, boneless breasts another, and backs, necks, bones with pieces of meat, and wings are boiled to make soup. I even prefer it this way, because a whole chicken makes so much soup my family gets bored from eating it day after day.
Put your chicken or whatever parts you use in a six-quart or larger pot. It will hardly fit in a smaller one. Cover the chicken with cold tap water. Put a lid on. Cook it on high heat until it boils. Once it boils, take the lid off and remove the foam with a spoon. Reduce the heat to very small, add a couple of large whole carrots and a large onion. Half the onion and cut off the root, but do not peel or cut it: you will remove it later. Onion peel adds nice golden color to your broth. Celery root and stalks, parsnip, parsley and bay leaf belong here, too. Let it simmer on low heat until the chicken is done, about an hour and a half. To check the chicken for readiness, poke it with a fork. You may quarter the chicken before boiling to make it faster, but it will make more foam to remove.
To keep broth clear, remove chicken and vegetables once the pot is safe to handle. You can proceed next day or even after that if you keep the broth closed in refrigerator. By the way, it's easy to remove excess fat then it hardened on top of cold broth. Remove meat from the bones. Cut a new carrot or two in fine (1/8") slices and add it to the broth. Add couple of sliced celery stalks and parsnip if you like. Bring the broth to boil, add salt and egg noodles, homemade noodles, small pasta, or matzo balls. Place the meat back in the pot. Cook until pasta is ready. Add finely chopped parsley and dill, ground pepper and garlic. Some people add fried finely chopped onion, but I don't like it. Makes ten to fifteen servings, depending on the rest of the menu. Note that herbs and spices are optional and interchangeable, the soup will be great with salt only. Rosemary, thyme and nutmeg are good additions, as well.
Clear chicken soup is same thing but with no noodles or pasta. It tastes great as well but not as filling. Serve it with crackers, wheat thins or knedle.