This addon works flawlessly, seriously. Read the readme and (assuming you don't make any silly mistakes), you'll have everything set up super quickly and easily. In addition, I had a problem and a suggestion for the addon that the developer added within 24 hours of my reporting. Great response time on support, great developer, and great addon to complement any server.
INSTALLATION
1. Copy the "discordintegration" folder into the garrysmod/addons/ folder which is where all of your addons are.
2. Navigate to garrysmod/addons/discordintegration/lua/
3. Edit the relay_config.lua file in the navigated directory (and discord_lang.lua for language configuration if needed)
Make sure to fill the required configuration parts and the modules you want to use.
4. (OPTIONAL) If your host supports binary modules, it is highly recommended to install GWSockets You can either find this binary module from your host's mod manager if it's added, or at this URL: https://github.com/FredyH/GWSockets/releases
Click at gmsv_gwsockets_<your server os>.dll and upload it to the directory garrysmod/lua/bin/. If you don't know what OS your server runs on, ask your host. You'll get a message in the console if the module loaded fine along of the lines "GWSockets is successfully installed!"
NOTE: If garrysmod/lua/bin/ directory doesn't exist, you'll need to create it.
5. Start up the server and everything should work fine