The first step is to install the enormous, proprietary Xilinx Vivado software. (Yes, all FPGA stuff is proprietary and strange). You can follow the general instructions here. The install took a total of 41GB of disk space (no, that is not a mistake), and took a few hours, but is otherwise straightforward.
The difficult bit was getting the Vivado software to actually see the hardware. It turns out that Xilinx use a proprietary USB driver, and, well, long story short you have to run the
install_drivers script buried deep in the Vivado directory tree. All it does is put a couple of files under
/etc/udev/rules.d, but it didn’t do
udevadm control --reload-rules so you have to do that as well, replug the cable, and it should be detectable in Vivado: