OK, the best help I can give is to say - throw it away!
This module is a really bad design. Sold to "beginners" who know no better!
It expects you to perform the multiplexing in code. That is in itself, do-able.
It uses 74HC595s to drive the displays. The schematic does not specify the values of R1 to R8, but to be within the specifications of the 74HC595, they would need to be about 1k8 each - what are they actually?
Go buy one of these:
Click for eBay listing.
Then we can give you good code for it. These give you a brilliant display, no multiplexing required as the MAX7219 does it all for you, you just feed it the data to display and that is displayed until you send alternate data, and the brightness is adjustable (in 16 steps). Unlike the one you cite, this is a proper engineering design.
I just ordered one of those MAX7219 displays! I did some research on this module and I think I will get this one to work quite easily. I will come back here if I encounter any problems.
Some may dispute it, but I think that is the way to go.
The MAX7219 - in the form of the 8 by 8 matrix modules - is pretty much the first thing with which I entertained myself with the Arduino (Pro Mini, by the way). That was a few years ago (five?) and is still sitting on the shelf beside my desk - or what is supposed to be my desk. At present, I cannot use it easily due to the things covering it, so I use this (my wife's) desk as my primary point to work on such things - and interact with this site. If too much of my stuff builds up, she clears it with significant prejudice. Anyway, the web browser on "my" computer refuses to be installed for some reason and as it is presently the mission-critical server, I cannot upgrade the OS - it is stuck on an old Fedora!
The long and short of it is that I have a repository of code which contains the routines to run MAX7219s quite comfortably, and are easily adapted for what you want.
What I do recommend, is that you also get one or two of these displays:
Which are used to display scrolling text and other basic animations. That can be your next exercise. You use Marco_C's "Parola" libraries ("MDmax ...") which can be installed using the IDE. Great fun.