The photos below will give the answer to this question.
First, the 2x8-pin female header provided with the kit needs to be replaced with a 2x8-pin male header (or two 8-pin male headers side-by-side). Place the header on the top side, as shown in the picture above.
Ideally, a "shrouded 2x8-pin header" (like this) should be used here, since that will also force the ribbon cable connector to be inserted with the right orientation (notice that the peg is closer the FTDI connector).
Then connect the board to the display using the ribbon cable (coming with the display), as shown in the next photo, and very importantly, paying attention to the orientation of the connector.
In case you wanted to chain a second display, just connect, with a second ribbon cable, the OUT connector of the first with the IN connector of the second.
The Wise Clock 4 software is able to correctly handle the second display if you modify this line in file HT1632.h, from
#define NUM_DISPLAYS 1
#define NUM_DISPLAYS 2
When fully lit, the current consumption of the displays are around 500mA. The best way to power them, especially when chained, would be through the terminal block, with the the red and black wires (as shown). In this case, the Wise Clock 4 board is powered from the display (through the ribbon cable), so you don't need to use an USB cable.
The easier alternative is to use the USB cable. This will provide power to the display(s) as well, but the voltage to the second display may drop below 5V, thus making it less bright, or even behaving erratically. Also, keep in mind that the USB port on a PC may not be able to supply the current for two displays (1A or so). If you notice problems with the second display, first step is to check the voltage to be around 5V.
NOTE: Make sure you use a 5V regulated power source. Anything above 6V will fry the board, and probably the display too. Also, make sure your power source is adequate for the power consumption. Use at least a 2A (10W) power source.