Can anyone give sensical instructions for using the new version of Do Not Disturb?

You can still hit a simple toggle switch to turn it on and off. They just moved it to the Control Center. To make it as close to the following as it used to be:

Go to Settings>Focus and delete all of the options except Do Not Disturb (and Driving, perhaps) by tapping on each one, going to the bottom of the screen and tapping the delete button.

Then, when you go to Control Center, you can turn DND on or off by tapping on the little icon of the crescent moon on the Focus button. That will turn it on. Tapping on it again will turn it off.

Don't tap on the word(s) on the button or you'll bring up that menu in the pictures above, which I don't think you want.

Yes, Focus is more complicated than the old Do Not Disturb but, I think it's well worth the effort to learn how to use it as it is far, far more flexible and useful once you do.

See also:

Use Do Not Disturb with Focus on your iPhone or iPad - Apple Support

Open the Control center and Turn On and off all focus (DND, Driving, Work, Sleep, Personal, Any other).