I have made many a pot of chicken and dumplings, and it's not difficult to do at all, just takes a little practice to refine the technique. I don't have a measured recipe, but I play it by ear. Generally, I use about a quart of broth, and I like to add some garlic and minced onion which have been sauted a little first.
Basically, heat your broth to a simmer. I use evaporated milk to make the "creamy" color for dumplings, and what I do is take a 2 cup measuring container and put about a cup of evaporated milk in it, then I add about a half cup of flour into the evaporated milk and incorporate it well. Add that to the broth and stir with a whisk, and continue to whisk occasionally until the broth mixture starts to thicken.
For the dumplings: (dumplings are very easy to make- similar to a biscuit dough)
2 cups flour
3 tsp baking powder
1 tsp salt
1/4 cup shortening (cut in to dry ingredients)
1 cup milk
I just mix the dumplings and roll them out like biscuit dough, but I like them thin. I use a pizza cutter to cut them into small squares.
When your dough is ready and cut, drop the dumplings into the simmering pot and let them simmer for about 10-15 minutes, then add the diced chicken (or turkey) into the pot, and stir it all together. Turn off heat.
You may need to season to your own taste with salt and pepper. These are pretty plain southern-type dumplings, but are always a big hit in this part of the country.