Apple - How does Keynote decide which display to appear on?

More recent versions of keynote don't have that preference. Instead: start the presentation. On the presenter notes screen you'll see these icons:

Click on the one that's second from the right (that looks like 2 screens being switched :-)

In Keynote's prefs, under the "Slideshow" tab, there's a pair of radio buttons to set which display to do the presentation on, and which to do the "presenter view" on. Took me a while to find it too, but there it is!

I did a google search finding this thread because I had the same issue as Bill Nace. I didnt find the answer anywhere so I thought I would share how I resolved it after trial and error.

Keynote seems to open the presentation on the display with the highest resolution.

Since my 'projector' display was the largest resolution when I would open a new keynote file it would open on that screen and then I would have to drag it back to the 'laptop' screen for any editing before starting the presentation. I increased the 'laptop' screen resolution and the keynote files started opening on that screen.