It occurs to me there are many ways to make chicken soup from scratch, but here is the way I do it, and it's pretty foolproof.
1 whole chicken, liver, etc. removed
12 c. water
2-3 whole carrots, cut into 3 pieces
1-2 onions, peeled and left whole
1-2 stalks celery, cut into 3 pieces
Put all of it in the pot. Bring to boil, skim off the scum/foam that collects on top. Reduce to simmer and cook for 2 hours. Remove chicken and set aside. Remove vegetables and toss.
At this point, I add 1-2 chicken bouillon cubes. I pull the chicken off the bone and add it back to the broth, along with whatever vegetables (usually baby carrots, chopped, onions and celery).
I cook my noodles on the side, because I have issues with them sucking up all the broth. Also good if you want to make matzo ball soup.