I'm not entirely sure how FPGA's work...
Do I simply buy a ZTEX and it mines, or do I need to plug it into a computer via USB?
Can I chain them?
I'm so confused.
The very basic idea of an FPGA is that it can be loaded with a specific firmware (a layout of logical gates, in essence). That page contains the firmware you'd need to load onto a Xilinx FPGA (A Spartan 6) in order to use it as a mining device. ZTEX refers to a suite of the FPGA, and various IO controllers (USB, etc.).
Roughly speaking, the steps you'd need to follow would be:
To answer your questions: yes, the device would need to be plugged in to a computer using the method in your link, and yes, you can "chain" them - i.e. have more than one plugged in. I've greatly oversimplified steps 3 & 4, by the way.