Chas, I would love for you to teach my turning class for a week or more. I'd be right in the student section learning along with the rest!
Jonathan, you would probably be shocked at my methods and approach to turning, the only thing that registers with me is the finished item, how it's constructed and tools used are all done on what might be termed 'lowest common denominator' basis in both work involved and costs.
DIY level 14" Bandsaw, but fitted with the best blade I can buy and tweaked to cut true.
Low budget chop saw, but fitted with good blade and adjusted for as near perfect angle and squareness to table that I can achieve.
Lathe tools, use as few as possible and as basic in form as possible from a good manufacturer, but no exotics.
Only work on wood during preparation if it actually needs it for next process.
Same with finishing, as these are buffing wheel finished, just sanded to 240grit no point in going further.
Look at the clamped bits in post above for next little boxes.
The Oak top and bottom is as cut out from previous larger box tops, just dressed each side for mounting socket and foot and mating surface for ring. The walnut ones rough cut on bandsaw from scrap and likewise socketed and mating surface prepared.
The rough clean up of those rings and the two pairs of top/bottoms took about 45mins including changing chucks between Cole Jaws and Dovetail.
(work saving tip here, Cole jaws are fitted on a 5" chuck so they give much wider range without moving buttons)
Note there's no attempt to make the components or work surfaces not needed for accurate fitting look pretty, just trued up enough to provide alignment guides.