Steps to get your adapter working if you've never used the adapter before in Mac OS 10.11 El Capitan.
Uninstall the dozens of other drivers you may have installed in the process of trying to get this working.
Unplug your USB adapter, and reboot and give yourself a clean slate.
Reboot. As soon as the screen goes black, hold down "Command" and "R" until you see a black screen with an Apple logo and a white progress bar. Let go, and wait for your computer to boot into recovery mode.
From the top bar, select "Utilities" and then "Terminal"
In the terminal, run csrutil disable.
From the top bar, select "", then "Restart"
Once you're booted back up, download and install the drivers from the CD, kindly uploaded by this fine human being.
Reboot.
Open your terminal, and run sudo kextload /System/Library/Extensions/USBCDCEthernet.kext
Reboot.
Plug in your USB Adapter, with a live ethernet cable.
Open System Preferences, and go to the Network Pane.
Hit the + button in the bottom right, select the "USB 2.0 10/100M Ethernet Adapter", and hit add.
You're all set! Your adapter works!
Apologize to the people you care about for the things you've said over the past few hours. They won't understand, but they will forgive you.