a) picture plane
b) top view (plan)
c) side view (elevation)
d) projection lines
s) station point
h) horizon line (aka eye level)

Perspective Projection of a point in three dimensional space onto a two dimensional plane is achieved by drawing a line from a station point to the point in the three dimensional space and finding where the line intersects with the picture plane.

This needs to be done once for the top view and once for the side view.

Having found the intersection with the picture plane in both views, parallels can then be extended from those intersections.

The projection of the three dimensional point is found where those parallels intersect.

further reading:

• Perspective