For the wiring, I did the following:
Power Supply: I connected the GND of my Arduino to the GND of the level shifter and then connected that to the GND of my ESP8266 to ensure they all share a common ground.
Level Shifter HV Side (High Voltage): I connected the HV pin of the level shifter to the 5V pin on my Arduino. Then, I connected the HV1 pin of the level shifter to the TX pin on my Arduino.
Level Shifter LV Side (Low Voltage): I connected the LV pin of the level shifter to the 3.3V pin on my ESP8266. After that, I connected the LV1 pin of the level shifter to the RX pin on my ESP8266.
I will draw later on a schematic and show it.