void setup()
{
  pinMode(9,OUTPUT); // LED output
  pinMode(6,INPUT); // Button input

  //... rest of the calculations and oled code...

}

void loop() {
  calculateYMD();

  while (digitalRead(6) == HIGH)  // sit here as long as the switch is LOW
    ;

  digitalWrite(9, LOW);

  display.setCursor(0, 0);
  display.print(Y); display.print(" God");
  display.setCursor(68, 0);
  display.print(M); display.print(" Mj");
  display.setCursor(25, 18);
  display.print(D); display.print(" Dana");
  display.display();
  
  delay(5000);
  
  digitalWrite(9, HIGH);
  display.clearDisplay();
  display.display();
// AND don't you need a display.display() call here?
}