How can I connect a Mac Mini to a VGA monitor?
It depends on which version of the Mac Mini you have. According to this Apple Support KB article, older Mac Minis can connect with a normal DVI port, which you can buy a DVI-VGA adapter for.

While the generation after that offered Mini DVI and Mini DisplayPort outputs, both of which can be adapted to VGA output. 

Then immediatly after that there was a generation that offered HDMI and Mini DisplayPort output options, only the Mini DisplayPort could be adapted to VGA output.

The current Mac Mini uses HDMI or Thunderbolt(which is compatible with Mini DisplayPort) for output. Only the Mini DisplayPort / Thunderbolt output can be adpated to VGA output 

Why no VGA on HDMI that is found here KB article:


  Can the HDMI port drive analog displays (VGA displays for example)
  using adapters?
  
  No.  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.


For Mac Minis with the Thunderbolt or Mini DisplayPort, the Mini DisplayPort to VGA
adapter would be the same as that used by MacBooks.

Third party adapters are also be available and at a lower price usually. A good low price source for compatible cables and adapters is MonoPrice.com