Question: I am tired of using canned broth/stock and would like to make my own - any suggestions as to the proper technique and parts to use?

Answer: 
I find whole chickens to be cheaper than the parts (wings, backs, whatever), so I regularly buy a couple whole birds, chop the breasts out (saving for later use), and then make stock with the remaining meat/bones/skin.

Place the chicken in a stock pot. Add a couple onions, carrots, celery stalks and some peppercorns. Cover with cold water. Bring to a bare simmer and cook for 2-3 hours. For ease, I usually bring the pot to a boil on the stove top, and then transfer to the oven at 250.

Strain the stock, chill, and then freeze for later use.
In general, the parts of the animal to be used in making stock depends on the animal:

For chickens, different people will recommend different parts of the animal, but simply chopping up an entire chicken works fairly well.

For beef, pretty much any tough piece of meat will work; try looking at shoulder or butt.

As for other suggestions, be creative! Almost anybody can make a basic broth by boiling a chicken, but making one that is truly fantastic takes time and work. Try adding different ingredients. For starters, try things that you are familiar with. For example, vegetables and herbs like garlic and basil can improve any broth. From there, try things that are more creative, like sesame oil, miso paste, or perhaps ginger.