Hi suzi1967, welcome to Apple Discussions!
There are a number of things we can try to resolve the problem here. The very first thing you should do is make sure you download and install the Mini DisplayPort to VGA Firmware Update. You'll need to have the mini-DisplayPort to VGA adaptor (the 'special connector') plugged into the MacBook Pro for it to work, as it actually updates the software on a chip inside that adaptor. You don't need to have the projector plugged in as well during the update, just the adaptor itself. I updated mine in this way with no problems.
Once that update is complete, plug the projector into the MacBook Pro. Ensure that the projector's input setting is on the correct input. Then, open System Preferences, and click 'Displays'. I recommend that if you do any work with projectors or external displays at all you check the 'Show displays in menu bar' box at this point. That will put a menu in your menu bar with a picture of a display on it. You can close System Preferences now. Then click that menu, and select 'Detect Displays'. The displays may flicker at this point. After that, you should see some picture on the projector. Using that menu, you can then change the resolution of the displays, turn 'mirroring' on or off, and 'Detect Displays'.
Mirroring means that both your MacBook Pro display and the projector will show the same image. If you turn off mirroring, then the MBP will go to 'extended desktop' mode, and will use the projector as a 'second' desktop. That means you can drag windows or icons from one desktop to the other, and have separate things on each display. Mirroring is simpler though.
If you have any questions, feel free to ask! And let us know if it works!
--Travis