This is where we can see the benefit of ascertaining the family of each and every plant, because already, (prior to starting this new system), I've made a blunder. You'll see I've got Apiaceae in all 3 of the West beds. That's because they've each got a row of coriander, which should of course have gone with its cousin, carrot, in the Midwest bed. Lamiaceae also appears in two of those beds, because I've planted sage in the Midwest, and oregano in the NW.
See? It does work. The coriander, sage and oregano bungles probably won't matter long term, and have taught a valuable lesson, (the puzzle over where the hell herbs fit into a rotation got me thinking about this in the first place). The point is now to make sure no bed has the same family planted in it 2 year's running, but should get a break from it for as many seasons as possible, preferably 2-3.
The schemes for crop rotation you can google online try to be simple, but, paradoxically, are hard to understand. This way, it's a question of puzzling it all out each spring, paying regard to what families have been grown in previous years, including winter crops and green manures. You need to have a way of keeping a record, such as a blog, and to be able to identify any plant's botanical family, which is easily done with Wikipedia.