A Determinant is an operation on a square mathematical matrix. There are entire college courses on matrices and determinants (especially since they are powerful tools for 3D computer graphics). But all you need to know are two things: [a] how to use a determinant to draw a nomogram and [b] how to turn an equation into a determinant.
This page will just cover drawing a nomogram from a determinant.
Here is a skeleton of a three variable determinant:
   X(a) Y(a) 1     X(b) Y(b) 1  = 0    X(c) Y(c) 1   
X( ) and Y( ) are functions, which in this case means its a fancy way of saying an equation with one variable. The variable is the one inside the parenthesis. X(a) and X(b) are totally different equations. For instance, X(a) might be a^2/(a1) and X(b) might be b.
Here is an actual real live determinant:

= 0 
It solves the quadratic equation az^{2} + bz  ab = 0 (as if you care) and has functional moduli that will fit it within 16 inches by 16 inches, a = +20 and b = + 25.
How do we draw it?
First we just look at the important part of the determinant:
X coord equation 
Y coord equation 

a scale  0.4 * a  0 
z scale  0.42 * z  0.32 * (z^2) 
b scale  0  0.32 * b 
As you can see, the top row plots the a scale, the middle one the z scale and the bottom one the b scale. Each scale has two equations, one will calculate the X coordinate and the other the Y coordinate for a given value of the variable.
These two coordinates are used to plot a point for that value. Plotting is done with the Cartesian coordinate system.
Lets do an example to make things clear. We will plot the Z scale.
First make a table of X,Y values for the Z scale. You can do this by hand, but it is much easier to use a spreadsheet. Here is a sparse table for the Z scale:
Z values  X coord (0.42 * z)  Y coord (0.32 * (z^2)) 
5  2.0  8.0 
4  1.6  5.1 
3  1.2  2.9 
2  0.8  1.3 
1  0.4  0.3 
0  0.0  0.0 
1  0.4  0.3 
2  0.8  1.3 
3  1.2  2.9 
4  1.6  5.1 
5  2.0  8.0 
Here is the Z scale plotted on Cartesian coordinates:
The entire nomogram looks like this: