I think I know how to generate points with an x,y and z component but how would I display this on the screen to give a 3D image with a depth of field? Thanks in advance.
Look at the Opengl1 library examples. It's a huge subject. Also, depending on what you are trying to do, see the various game engines and the excellent tutorials put up by Informatix. The game engines wrap up a lot of the complicated stuff and present it in a way where you can actually do something with it.