How would you add Arduino WiFi Module using I2C or serial interface?
You would connect the ESP8266 to the serial port.  The normal way of working with an ESP98266 is to issue AT command (like an old Hayes modem) through a serial connection. Since you have one of those available on your board it is a simple matter to just wire it directly to it.

Just follow any of the myriad of ESP8266 + Arduino tutorials, substituting the pins in the examples for your serial pins, and use the Serial1 object instead of the SoftwareSerial class that you have to use on an Uno that lacks extra serial ports.