Using the built-in ADC

Voltage divider

The ESP8266 has a single 10-bit ADC pin and it's labelled A0. It only accepts input voltages up to 1V and so you will need to use a voltage divider to create 1V from the board's 3.3V. The circuit is shown here - resistor values of 10kΩ and 22kΩ are suitable, though you could use a variable 22kΩ potentiometer in order to adjust the voltage to more precisely to 1V to ensure that a full 1024 values are available.

You need to connect the 0V and 1V lines to the GND and VCC pins on your sensor and connect the output from the sensor to the ESP8266's A0 pin.