This is one of those recipes gets passed down from generation to generation and never gets written down. I'll make an attempt, however.
The best way to start is by cooking a whole chicken in a stockpot on the stove, taking the chicken out, letting it cool, deboning it, putting the chicken back into the stock, etc. While this yields the best result it isn't quick enough for your average weeknight dinner. Instead, I'll often make it with precooked chicken, or cut up chicken breasts and thighs.
Chicken Noodle Soup
1 Tbsp. olive oil
1 lb. cut up chicken breasts or thighs (or some of each) OR 2 c. cubed cooked chicken
2 carrots, peeled and chopped
2 stalks celery, chopped
1 tsp. dried thyme
1 tsp. salt
1/2 tsp. black pepper
1 Tbsp. dried parsley
8 c. chicken stock
1/2 bag wide egg noodles
*up to 1 Tbsp. chicken base (optional)
1. Heat olive oil in large pot. Add chicken and cook until nicely browned. (skip this step if using precooked chicken.)
2. Add vegetables, thyme, pepper, parsley. Cook about 5 minutes, stirring occasionally until vegetables soften.
3. Add broth and bring to a boil. *Add chicken base.
4. Add noodles and cook 8-10 minutes until noodles are done.
*Chicken base is NOT the same as bouillon. A good chicken base will have the first ingredient listed as "chicken." You may want to use it if you have a very weak flavored broth...such as a low sodium, low fat variety. Taste the broth first (before it is boiling) and if it doesn't have enough good chicken flavor, then add the base while the stock is boiling. It will dissolve best that way.
Remember that a little goes a long way.