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 serve rotisserie chicken once in a while - I save the bones in the freezer until I have enough to make a big batch of stock. I also save the tops and bottoms of celery stalks and other trimmings when I make veggie trays. The veg may get mushy from freezing but it still has great flavor to add to your stock. I find that for home use freezing the stock in 1-cup increments works great.
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.