For chicken & dumplings: Cook chicken in a large pot - cover it with water. Chop some onions, celery and carrots to put in the pot with it. Add salt/pepper. If you have some herbs (fresh or dried) such as sage or parsley - add a little of that, too. Boil it gently until the chicken is thoroughly cooked. What I call "scum" will form on the top of the boiling liquid. It won't hurt you - but it doesn't look wonderful. So I skim it off as the chicken cooks. Once the chicken is cooked, take it out of the pot - leaving the broth & vegetables in the pot. Let the chicken cool, then take the meat off the bones. I usually chop or shred the meat. Set the meat aside.
Make your dumplings (lots of different recipes for dumplings. I mix self-rising flour with chicken broth, salt/pepper, and some chopped fresh sage. Mix it and then roll it out on a floured board. Cut into approx. 1 inch x 2 inch strips).
Set the pot (with the chicken broth and vegetables in it) back on the stove and bring to a rolling boil. If there is not enough liquid - you can add more chicken stock to it. Drop the dumplings in one at a time. No stirring. Once the dumplings have cooked, add the chicken back into the pot. And your chicken and dumplings are ready to eat.