The vanishing point is a
technique in
perspective drawing. The simplest use of the vanishing point is the one point perspective.
The first step is to define the vanishing point itself and the horizon line. This horizon line represents the eye level of the viewer and is where the ground and the sky meet.
 * 
All receding
parallel lines (known as
orthogonals) converge at the
vanishing point.
\ /
\ /
\ /
 * 
/ \
/ \
/ \
To draw a box with a single vanishing point style:
 * 
/ 
++
/ 
/ 
++
 
 
++
Notice, how the the lines that move away from our view point
converge to the vanishing point.
The two point perspective is used when looking at the corners of boxes and buildings (and other similar objects) and uses multiple vanishing points. This type of drawing starts out with a line and the two vanishing points at either end of the line.
*  *
Perpendicular to this line is the front most corner of the object.



* + *



From this point, the
ASCII art gets difficult. It follows many of the same rules of one point
perspective, however, lines that recede to the right converge at the right vanishing point, while lines that recede to the left converge at the left vanishing point. The box below is marked in
bold.
___.._
___.'  ._
_.'    `.
* + *
`._    __'
`.______  _.'
`'
It is possible to use multiple single vanishing points in a single drawing. The most often instance of this is with a road vanishing into the distance, but turning (not a straight road as seen in the desert). Each twist of the road leads to a new vanishing point.
See also:
http://www.olejarz.com/arted/perspective/
http://mathforum.org/workshops/sum98/participants/sanders/Geom3D.html