Wiring is thankfully fairly simple, much easier than trying to actually wire up 6 x 8x8 matrices. The HT1632C driver chip requires only 3 data pins -data, write, and chip select (cs). You can't skip using cs like many 'true' SPI devices. One of the nice things about these chips is that they are designed to be used in multiples, so you can share the data and write pins. However, each HT1632C must have its own cs pin! So if you have one display, you need 3 pins, two displays need 4 pins, three displays need 5, etc.
Lets assume you'll be using a single panel to start (and then show how to wire up multiples).
Begin by plugging in a 2x5 pin IDC cable into the top left socket:
You should also check that the J5 solder jumper is 'filled' with solder - you need to have J5 shorted for using one or two panels in a cascade. Use a soldering iron to heat up some solder and melt it on to J5 if it isn't filled yet.
Next, you will need a few wires, we will use the following convention: a Red wire for VCC (+5V), a Black wire for Ground, a White wire for CS0 (chip select #0), an orange wire for Data and a yellow wire for Write. Make sure that when you look at the other side of the IDC cable to plug in the wires, you have the connector arranged right, the red stripe on the IDC is on the same side as the red wire for VCC.
Finally, you can wire the panel up to your Arduino. You can use another microcontroller, if you adapt the code but we will use an Arduino.
Connect VCC (red) to +5V, GROUND (black) to Ground, DATA (orange) to digital 2, WRITE (yellow) to digital 3, and CS0 (white) to digital 4.