If needed, you can download the latest driver from their respective manufacturer's site. Though there's few report regarding manual driver installation to get the adapter working properly. There should be no need of driver installation on macOS 10.9 and above. As default inbuilt USB to Ethernet driver has a wide range of hardware support.
Recent versions of Linux, Android and Chrome OS also doesn't need any driver installation. But Windows 7 may require manual driver installation, specially when not updated. Most of the usb to ethernet cable listed below doesn't need any kind of driver installation on Windows 8 or Windows 10. Driver compatibility: It's the first thing you should consider before buying.