How do I show what's on my computer screen on a projector?

To show what's on your computer screen on a projector, you must go to the Displays pane in System Preferences.
Apple Menu System Preferences  
Displays pane  
Go the Arrangement tab and choose the "Mirror Displays" checkbox.
Mirroring in Displays Pane  
Otherwise if left unchecked, your computer will display an extended desktop.  You'll notice when it's unchecked that you can move the cursor and windows to this extended desktop.  An extended desktop is more useful when you've got an extra monitor that you want to attach to your computer.