Here is the spreadsheet. I didn't add all the fancy labels because graphs with Excel are a PITA. Learn MATLAB or, for free, learn Octave, an opensource work-alike.
In any event, it shows the characteristic curve we expect as a diode gets increasingly forward biased. Print the graph and just use a pencil and straightedge to estimate the resistance R = E / I. You pick a couple of points on the slope of the line, figure out the change in current and the change in forward voltage. Do a little division and you get the dynamic resistance. It will be a low value of Ohms. Around 4:30 in the video...
As to the theory of the junction, that stuff is all over the Internet.