As stated in the description of this deviation: Minimum knowledge of the software required.
This means being able to navigate through the software
and understand more or less what you're doing, a basic use of the editor
(the bunch of triangles you're talking about) and how to set and start a rendering process
To get started with Apophysis, I suggest you Starting Out: Learning Apophysis
, which is the most recent guide I found on deviantART, and provides you with links to other useful tutorials.
The problem with your render is that it's a transparent PNG, and to solve it you simply add a dark background with a photomanipulation software (like GIMP or Photoshop) or you change the settings in Apophysis itself (by turning the PNG Transparency off).