buy a whole chicken and chop it up then throw it in a pot of boiling water. If it had a liver with it try and see if your cat will eat it but don't put it in the soup.
You want enough water cover the chicken by an inch or so, you can always add more later if you need to. Add a table spoon of salt and boil for an hour or so. Boiling longer gives it more flavor but the meat starts to fall apart.

After it has boiled removed the chicken and set it aside to cool. Scoop some of the fat off the top and if you have a screen strainer you may want to go ahead and strain the broth. If you don't use a spoon to fish out any unwanted bits and if you have ugly brown stuff on the side of the pot scrape that off as well.

Chop and add an onion, 2-3 carrots and celery sticks. Add a bay leaf or two and bring back to boil. Boil for 30 min or and by now your chicken should be cool so take the meat off the bones and throw away the bones and skin. Add the chicken back to the pot and bring it all back to a boil. You are going to need a fair amount of liquid for the noodles so add 3-4 cans of chicken broth. If you don't have broth add water and bullion cubes (4-5). Add about 3/4 of a package of wide egg noodles and cook for 7 min. Add salt and pepper to taste.

Sorry I don't have exact amounts but I just eye ball it. You need a good sized pot. The tricky part is the noodles soak up a huge amount of water so it is better to err on the side of to much liquid instead of not enough. I fill the pot up and 4/5 of the way and just leave enough room for the noodles.

This makes a large amount of soup if you don't want that much or don't want to mess with a whole chicken you can use breast but then all the liquid needs to be broth or it will be tasteless.

I am a big soup fan so if there is any particular s type of soup you want I can probably recommend a recipe.