This article states "The HDMI port will drive digital connections—such as DVI—using the adapter that came with the Mac mini, but cannot be used for analog displays such as VGA. You can purchase a Mini DisplayPort to VGA adapter separately to drive analog displays."
If you follow these instructions, you will be deeply disappointed.
Apple Mini DisplayPort is NOT the same as HDMI.
To drive a VGA monitor, you must purchase an HDMI to VGA converter. This is a $60 digital to analogue conversion box.