connection for hall sensor 4 pin and arduino nano
The board you have has two outputs - AO and DO (note, those are the letter O not the number zero - for output).

You can connect AO to any of the analog inputs on your board if you want to read a discrete analog value from the sensor.

You can connect DO to any of the digital inputs (or analog ones since they are also digital inputs) if you just want a simple "Something is there" signal.

The sensitivity of the "something is there" is controlled by the trimmer on the board. 

The simplest way of doing what you want is to use DO and adjust the trimmer to suit. Then the sensor looks, to all intents and purposes, like a switch or a button (but you don't need the pull up / pull down resistor).  So you can leave AO disconnected.

Note that using D0 (zero) and D1 (one) on the Arduino is discouraged since they are connected to the USB interface and using them can affect your ability to upload sketches. It also means you cannot use any serial communication in your program.