Let's assume you have a new generation pressure cooker (not that crazy thing your grandmother used). Before closing it up for the pressure cooking part, we're going to take a few minutes to brown the vegetables and chicken to develop some wonderful flavor that will transfer to the stock as it simmers.
Remove these and follow with the onion just long enough to brown.
Now add everything back to the pot and cover with water, at least 4-6 cups. Throw in 3 or 4 garlic cloves. They don't need to be peeled, just smashed a little. Some fresh parsley and a few sprigs of thyme are also good.
IF you're using a pressure cooker put the top on now and bring up to pressure, lower the heat, and cook for 30 minutes. You will not believe how rich and deep the flavor will be in this broth! The pressure cooker drives flavor into the food rather than losing it to evaporation. The controlled high temperature creates a browning reaction that makes for amazing flavor development. (If you are using a stockpot instead, cover now and simmer - don't boil! - for 3 or 4 hours. You will probably need to start with more water also, 8 cups or so, since it will evaporate.)
|(Only 30 Minutes later in the PC)|
|(Straining the broth through cheesecloth.)|