I purchased this module as part of a microcontroller kit, its an interesting little module as it has 16 buttons but with only 1 I/O line is required, an analog input. You connect this to your Arduino and read in the value.

The concept is straightforward  you use a resistor network as voltage dividers, and then let each button feed a different voltage to the analog pin. So by detecting the voltage you can tell which button has been pressed. You can only detect one button at a time

AD Keypad

Here is the schematic of the module, hopefully you can see what I described earlier

AD Keypad Schematic

Code

I put in a slight delay to try and compensate for bounce on the key press which would result in multiple values returned

Source code

#define KEYPAD_PIN 0
 
// milliseconds to wait, to make sure key is pressed
#define TIME_TO_WAIT 200
 
void setup()
{
    Serial.begin(9600);
}
 
void loop() {
  // put your main code here, to run repeatedly:
    int reading1 = analogRead(KEYPAD_PIN);
    // waiting
    delay(TIME_TO_WAIT);
    // reading 2nd time - to make sure key is pressed
    int reading2 = analogRead(KEYPAD_PIN);
    if(reading2 <= 1000)
    {
      Serial.println(reading2);
    }
}

Output

Pressing the keys from K0 to K16 outputted the following in the serial monitor

0
61
125
190
253
316
380
447
510
576
641
702
765
831
896
960

So using a switch case you can use this module in your own examples, best practice would be to have a high and low value and check between the range

Links
AD Keypad 16 Push Buttons 4×4 Accessory Board Matrix Buttons