I am trying to look for a feature that allows me to add submodules to one of my modules, but I can't seem to find it on the GitHub website. Is this something that I'll have to use the Git shell for?
It has "built in" support for submodules, github is just a visual GUI for the git protocol, which is not made or owned by "GitHub"
If their GUI doesn't provide for some kind of drag-and-drop way to link a submodule, then you have to use the command line or a different GUI to do it. Once the submodule is set up , however you do it, github will be able to show it to you