You need the pulldown resistor from the input pin to ground to prevent the switch from floating (in an undefined state) when the switch is not pressed (open). The value of the resistor is not critical. 1K to 100k will be fine with 10K being the usual value. It will also help (but nor necessary) to put a 0.1uf cap across the switch (so input pin 6 to 5V). That will help to debounce the switch and prevent spurious counts.