How to debounce two buttons and LED?

Using Arduino LEDs and Multiplexing
4

Start here:

const int buttonPin_1 = 2;  
const int buttonPin_2 = 3;
const int ledPin = 13;   

int ledState = HIGH;
int buttonState; 
int lastButtonState = LOW;

long lastDebounceTime = 0; 
long debounceDelay = 50; 

void setup() {
  pinMode(buttonPin, INPUT);
  pinMode(ledPin, OUTPUT);

  digitalWrite(ledPin, ledState);
}

in the setup() you have set neither button_Pin_1 nor button_Pin_2 for INPUT.

added: you should have noticed something was wrong when you couldn't successfully compile this, btw.