The best & normal way is just as johnwasser shows you in reply #1. You don't connect the button to +5v, just connect the buttons between pins 2 & 3 & ground. johnwasser's code is looking for a ground on pin2 or 3 when the button is pressed. The code in setup()
pinMode(UP_BUTTON_PIN, INPUT_PULLUP);
pinMode(DOWN_BUTTON_PIN, INPUT_PULLUP);
uses INPUT_PULLUP to use a resistance internal to the chip that makes pin 2 & 3 +5V when the button is not closed.
Just change
const byte LED_PIN = 13;
to
const byte LED_PIN = 10;
and it will work just fine for you.
You do not need the 10K resistor using this method.