The GL819 from Genesys Logic is a USB Card reader.
The connection from this PCB to the printer electronics is via 4 wire USB, completely standard.
The only way you are going to use this with an Arduino is via an USB shield and some kind of library for Mass storage devices (i don't know if that exsists)
The chip on your PCB is in the 128 pins LQFP housing. Pin 25 is your USB D-, Pin 26 is USB D+
Regarding power, the GL819 wants 3.3V - not 5V as the Arduino usually uses.
Look if there is a voltage regulator on the card reader PCB, if not you'll have to give the board 3.3V your self.