Help setting up RFID reader with hard to understand schematic with arduino UNO

This setup is using Serial, not Wiegand. The third pin (the one next to the two antenna loop pins) is connected to +5V so it is HIGH. The description clearly describes the pin as "3. high-level election serial port, low-level selection of Wigan, not vacant"

If you are connecting to an Arduino with a spare hardware serial port (Leonardo, Micro, MEGA) then use hardware serial. Otherwise use SoftwareSerial.h. Connect Pin 5 (marked TX on the board) to the RX on your Arduino. I don't see any baud rate specification so try everything from 9600 on up until you receive clear data when a card is detected.