How to do plane coordinate transformations?

I was wondering how to "fit" together two different coordinate systems (eg. camera coordinates to real world). I tried to find some theory, but this is best I could found: https://www.e-education.psu.edu/natureofgeoinfo/c2_p18.html - particularly the "Second-Order Polynomial Transformation" looks like what I'm trying to do. However there's no explanation how to do that.

Where and what I should look?

Edit: This is best reference I've found so far: http://btcsure1.ferris.edu/NGA/Nick_2D_Tran.ppt