To me, the most important insight of the Covey quadrants is that you must choose to make time proactively for QI actions that are important but not urgent. You can't just wait for inputs. Calling my mother, writing a note to an old friend, exercising, planning for the future. . .all things that never have to be done today but pay off hugely when I consistently do them over time.
I don't have any formal way of using the quadrant priority model, but I have been evaluating potential actions in terms of importance and urgency for so long that this way of thinking just seems natural to me now. It acts as a first-pass filter to make sure that QI items are on my lists, and to keep QIII items out of my lists.
QI fits into my GTD-like workflow model: a QI Covey goal such as "Be a good spouse" must be implemented by a series of actions, consistently sustained over time. Covey advocates a focused weekly planning session in which you specifically plan and schedule QI actions -- things that never seem urgent but require initiative to achieve goals. GTD advocates a weekly review/planning session in which you think about everything from the runway on up to 50,000'. GTD assumes you will review important things, urgent or not, while Covey assumes you could easily neglect important, non-urgent things. So Covey gives you a little kick in the pants to think about those specifically. Thinking about everything GTD-style is great -- unless you skimp on it and neglect QI which requires your own initiative.
If you spend some time thinking about your long-term goals and figuring out how to translate those into actions to achieve them, that's the essence of Covey IMO.
In the past, I had problems with the Covey quadrants because I had an ineffective way of estimating importance. I recently asked myself, Can something be urgent but not important (QIII) and yet I still should choose to do it? My answer was No, if I choose to do it, it must be important somehow. Importance is determined by my commitment, not by whether I self-generated the action or by how I personally feel about it. For example, I have a commitment to attend certain meetings that I personally did not call, that I don't "feel" are important; but they are important simply because I have made a commitment to the people or organization involved. Keeping that commitment is important to my integrity. So despite my feelings about it, the meeting is truly QII. I have plenty of QI and QII things to do; I never want to do any QIII -- life is simply too short. If something is urgent and I have no commitment, I will not do it (for example, going shopping just because there is a sale).
The routine maintenance items such as Katherine mentioned also used to trip me up because I always underestimated their importance. When you don't sufficiently maintain the well-being of your physical self and physical things, in the long run the "more" important stuff will suffer. It turns out that doing laundry IS important. Changing the oil in the car IS important. Taking care of my physical body IS important and actually eats up a lot of time, too. This type of action is deceptive because it doesn't seem that important in itself, but is critical to support important goals.
In the balance of life, I have also underestimated the importance of QIV activities because they often do contribute to rest and renewal. QI and many QII activites -- the things that are important -- often require a lot of energy. Whether mental or physical, energy must be renewed by periods of rest. I cannot work 16 hours a day on my QI and QII stuff, at least not day in and day out indefinitely. I'm too old for that now! I have in the past broken my health by expending too much energy without renewing it. I must intersperse high-effort tasks with low-effort ones, and this is where QIV fits. (QIII does not because of the stress of urgency, at least for me.)
For me, reading and writing posts on this forum is a QIV activity because it is low in importance relative to the stuff in QI and QII and of course low urgency. But I choose to do it because I do benefit from the activity itself, plus get rest from the stress of QI and QII.