The way I learned the zone system was fairly simple. It required the use of a spot meter, which you used to get an accurate sense of the dynamic range of the composition. There are 10 zones, each an EV or stop apart.
I was taught to pay particular attention to areas that I wanted to be sure had detail, whether in the shadows or the highlights, as these areas were vulnerable to being pushed outside of the workable dynamic range of the film. On the spot meter scale where you translate the EV reading into f-stop/shutter speed combinations, there are marks for each EV on either side of the main mark, which is 18% gray or zone 5. I became most interested in shadow detail (not caring if highlights were blown out), so I tended to overexpose for the shadows, making sure they didn't fall below zone 3 more or less. So my method was basically spot meter the shadows, take that EV value and place it around the zone 2 or 3 mark on the spot meter scale. The next step, which I didn't do because I generally care less about highlights and, as I said, don't mind blown highlights, would be to see where this placed the metered highlights on the EV/zone scale. Accordingly, you might need to pull development if the highlights were placed beyond zone 9 or so.