Here's what I do. I don't actually measure anything, but it's a forgiving recipe.
Put dark chicken pieces in the crock pot. (I use skinned thighs, but you can leave the skin on if you don't mind the fat.) Add some carrots (either baby carrots or carrots cut in half), celery, and onion. Also add about a cup of chicken broth. Cook on low until chicken is done (usually about 8 hours or so).
Take the chicken off the bone and shred it with 2 forks. (If you want to reduce the fat, strain the broth and put it in the fridge for a few hours or over night, and then scrape the fat off.) Combine the chicken, veggies, and broth. The broth is almost double-strength, so add water to taste. Also add pepper to taste. Pepper is what makes chicken broth really good. You can salt it if you need to.
Bring mixture to a boil in a sauce pan. To make dumplings, combine Bisquick and milk until it feels like dumplings.
I think the amounts are on the box, but I just go by feel. I usually also add parsley to the dumplings. Use a spoon to drop clumps of batter in the soup, then simmer until done. I think it takes about 10 minutes. That part is one the Bisquick box, too.
If you want flat dumplings, you could probably use the canned bisquits that are in layers instead of Bisquick and separate each bisquit into about 2 or 3 dumplings.
I'm from the flat school of dumplin making. Actually, my mom makes the best ever. She rolls out canned biscuits until they are almost paper thin. Not sure exactly what the recipe is because she just does it. 
