The wiring is made for a special flat, flex cable socket. In the bottom drawing of the fan (the back) in the PDF and your photo, the top conductor (on the right end) is to your battery plus. The conductor below that is your battery minus. You can ignore the lower two conductors. You will need a way to solder two wires to the end of that cable. There may be others here that have done that, and can make recommendations.
Ken
Ken