Using solderless pins the adapter slides onto the back of a Pi Zero GPIO (If a permanent connection is required the adapter can still be soldered to the GPIO header).
The adapter PCB is printed with an alignment guide - ensure the white SQUARE on the PCB is aligned with the GPIO pin with the SQUARE gold pad on the Pi Zero GPIO pin 1.
It's advised to connect the adapter to the Pi Zero before connecting the USB cable to the adapter, once connected the Pi Zero can be powered on/off without issue (to prevent the serial RX/TX pins being connected before the ground pin).
An FTDI FT234X IC is used in the adapter. "Virtual COM port (VCP)" drivers are available on ftdichip for many operating systems, the required kernel module is automatically loaded on recent Linux installations.
When using with the Cluster HAT (as shown in the image above) you will need to cut the pins down (I used wire cutters) so only a few millimeters stick through the Pi Zero and then file the ends round otherwise the adapter will short on the back of an adjacent Pi Zero. With use the pins may become worn and need adjustment to keep in good contact with the Pi Zero GPIO header.
You are buying a single USB to serial adapter (Pi Zero / Cluster HAT / USB Cable not included).