Found this task initially tricky but once you get the hang of it, it’s quite obvious. Michael does mention it, but I think it needs to be more explicit and explained.
1/ You must start this task in EDIT MODE FIRST,
2/ Make sure snapping (by vertices or by element type) and auto-merge is enabled.
3/ THEN create a new object (shft-A)
4/ When you drag the new object to the active object it will snap and collapse any redundant elements on contact.
Gah! I found this older topic that also summarises my initial experience as well.