The following is a poor answer (since I am by no means an expert on the topic), but I decided to take a quick peek around and came up with this thesis: http://steve.hollasch.net/thesis/#chapter4
Projection of a 4D object into 3-space is, as you would expect, a simple extension on the projection of 3D into 2-space, and the above thesis demonstrates different kinds of projection from 4D to 2-space. The code samples are in C, so it should be easy to follow.