All right, sit down with a cup of coffee and a danish, as this is going to be a LONG read.
As many have said, your soup is ONLY as good as your stock. And I make killer stocks at home. Do a search for the thread I created about "Beef Stock 101". Use those words, with the quotes, and it ought to pull right up. WARNING: Lots and lots of pictures!
My chicken stock is made by roasting off chicken bones (I prefer to buy chicken leg-and-thing quarters, and save a lot of the scraps). I usually have around 10 lbs of scraps when I make a batch of stock. When all the boens are caramelized, I add them to my stockpot that's half-full of simmering water, along with a couple of onions, and several stalks of celery, all rough-cut. I don't really care for the taste of carrot in my chicken stock, so I leave it out. Fill with more hot water until everything is just covered, cover the pot, bring to a boil, then reduce to a simmer and let cook for about 12 hours (I usually cook chicken stock overnight). I strain the solids, then reduce the stock by about half to concentrate it, then chill it in an ice bath (see the beef stock post about how I chill it, it's QUICK).
Optional: When the bones are done roasting, pour off some of the fat into an empty stockpot, and caramelize the veggies. THEN add the bones, and water, continue as above.
Optional ingredients: Leeks make a great stock. I will also add sprigs of fresh sage, fresh rosemary, and fresh thyme if I have them, along with whole cloves of garlic. I have literally had waitstaff into the kitchen and tell me the members are demanding to know what I'm making, as they can smell it all the way out in the bar, and sometimes outside (if they're downwind of the exhaust vent)
I'm in a bit of a situation right now, as I am completely OUT of both beef and chicken stock. I never produced chicken scraps, as all summer long I've been grilling and smoking chicken. I do have some scraps that I've generated in the past week or so, as well as a small quantity of beef bones. I will be making more stock in a week or two. Heck, I might make a basic batch of vegetable stock just to tide me over.
One tip I can give is this: I made chicken rice soup last Monday. No stock, and RAW chicken. I poached my leg-and-thigh quarters until done, then cooled them in the fridge. I did keep the broth at a simmer, as I planned on using it for the soup, but had several hours to go before cooking (no "hot box" at home). When the chicken was cool, I pulled it off the bones. Bones went into a ziplock (scraps for the next batch of stock), and the SKIN went into a different bowl. The meat was rough-cut and place in another bowl. I started the soup off by rendering the fat from the chicken skin. This gives me fat to saute the veggies in, as well as imparting a "browned chicken" flavor to the soup. When the skin had rendered, the "cracklins" were reserved for another use, the "fond" was left in the pan, along with some of the fat. Veggies and seasonings went into the pan, and were sauteed over high heat until they just started to caramelize. Chicken broth and meat was added, brought to a boil, and simmered for about 30 minutes. The remaining chicken broth was used to cook the rice in. I leave the rice separate from the soup itself, as there WILL be leftovers, and I prefer to keep them separate, so the rice doesn't get all soggy overnight.
If you all haven't noticed by now, I usually caramelize EVERYTHING. I like how it deepens the flavor. Plus, when you're making a soup and just add raw meat to the liquid, it will get cloudy as the serum albumen from the blood gets cooked.