Its a Mini Displayport to VGA. I do see the Arrangement tab and I have selected Mirror. The projector just shows a Blue Screen. It will flash for a moment when I connect the adaptor but then just stays Blue. There is an error message about incorrect resolution but no matter what resolution I try it still does not work.
The "mirrored" choice would send the same resolution on the Projector that you have on your local screen.
If you get no video on the projector, have you tried another cable, or at least tried a different MDP to VGA adapter?
Make sure it's not a projector issue by trying another display, rather than the projector.
All else fails - try an HDMI to VGA adapter.
Just to double check - Turn Mirroring Off!
If the Arrangement tab shows both your local display and the second display, then it should work as an extended screen. The second screen (the projector) will be lined up along an edge of your local display - so try moving a window on your screen, until it mostly goes off the edge, into the second display. Do you see ANYTHING on the projector screen? The Displays window should ALSO show up on both your screen, and the projector screen, any time that pane is open.
You can try the Detect Displays, and see what happens, if anything. If you don't see a Detect Displays button on the Displays pref window, then press your Option key and watch the Displays pane.
Does ANYTHING appear on the projector screen?
Leave everything connected and the projector on. Turn off your Mac, so it goes completely off (not a restart, but shut down. Double check that video connectors are attached. Boot your Mac again.
Do you see anything on the projector screen after your Mac gets to the desktop?