Okay, so, what can I do with the BNC jack on my PC? I've got some BNC cables I found at work and about 50 other BNC cards laying around so I figured it was worth exploring.
Can I network two PCs together with a BNC cable? If so how?

HI Zachary the good old days lol you sure can but there daisy chain them then put a terminator at each end and configure as normal no router needed

Networking is a new thing to me so could you be more specific? How do I configure them?

I can't believe i actually found somewhere that still has instructions on how to set them up:

Networking Explained - installing a network in your home or small office
Setup Your Network 2

If you want to set up your own network at home and learn about networking then I would recommend buying a cheap 4 port switch as most pc's these days have onboard nics and it will be much faster than an old thin ethernet network.