Can not make presenter view work in Yosemite

Question

Can not make

Answer 1

Thank you for your help and patience. I'm trying to understand this so I can fix it if I get in the wrong situation again (which will be shortly before the crowd wants to see the talk).
I gave the same Keynote presentation on the same MacAir a week earlier, before switching to Yosemite, and everything worked the way I wanted. I installed Yosemite and either the default settings changed or Yosemite switched me back to default settings I had unknowingly changed.
I don't remember seeing the word "Extended" during the 10 minutes that I played with this while some of the crowd watched. I turned Mirroring on and off, moved the bar from screen to screen, turned gathering screens or displays (I forget) on and off—and could not get a combination that displayed the presenter view on my MacAir. I just checked Play > Customize Presenter Display and everything is checked or not checked correctly (i.e., I don't use the notes, and they were the only thing not checked).
I looked in Keynote help. "Extended display" and "extended" produce nothing on this. "Mirroring" and "mirrored display" produce nothing helpful, The section on "Present on a separate display" does say "If you’re using Apple TV and are mirroring your display, you won’t see the presenter display on your Mac," but I wasn't using Apple TV so that doesn't apply. Otherwise, it says everything will automatically be right — but nothing was automatically right.
So the next time I am connected to a projector, How do I switch to Extended display? I am certain that at one or more times I had Mirroring turned off, the bar on the left screen, and there was no presenter view. And I don't remember seeing the word "Exended," or ever having these problems in the past.
PS: I now understand what gathering displays does—it puts the controls on the computer rather than the other display. That could use a better name. There's rarely a reason to turn it off, but when you're trying everything why not try "Gathering" because who knows what that means? And that just slows the process down why you fiddle with controlling everything from a screen behind you.