I'd recommend finding a copy of Fred Picker's Zone VI Workshop book. I don't think it's still in print, but there are almost always copies on ebay and at used book sites. I think my library even has a copy. Fred, IMHO, did a very good job of boiling down the basics of the Zone System and getting one on the way to properly using it. Adams, again IMHO, goes into far more detail than one needs at the beginning.
The Zone System is, in large part, a way of thinking, and I believe Fred's little book is a great way to begin.