I'm not sure what mini you have...some have DVI ports (long with rows of pins) while others have mini-display ports. I think all have HDMI ports. Look at your mini and your VGA cable, if they don't match up then you'll need an adapter from Apple or Bestbuy or Amazon.
If you give more information someone here can show a picture of the adapter you'll need.
If you have a newer one it will have an HDMI video out and one Thunderbolt video out. You need a mini-display port/Thrunderbolt to VGA adopter