How do I share an internet connection through USB?

This is impossible, unfortunately. All USB connections must be between a host device (e.g. a computer) and a normal USB device (mouse, etc.). Desktops and laptops are always hosts and therefore cannot connect to each other. Some newer mobile devices implement the USB On-The-Go standard, and can switch between being hosts and normal devices, but this won't be the case for your computers.

Without any deeper knowledge, I would suggest looking at the Linux USB Project, section USB Host-to-Host Cables, and possibly Easy Transfer Cable (although that seems to be mainly a Windows thingy). In any case you are likely to need additional hardware, because the cable probably is not "just wires".