WS2812 LED Connect 4 Game, Please Help!!

One issue. Connect 4 has a 7x6 play grid, not a 6x6. Can you add 6 more LEDs to make the 7th column?

Another issue: Your code is difficult to read. When you are in the IDE, hit CTRL-T to autoformat. And get rid of unnecessary white space. I copied in your code, made these 2 changes, and now it is much easier to read.

#include "FastLED.h"
#define NUM_LEDS 36
#define LED_PIN 3
int  buttonPin = 8;
int  buttonState = 0;
CRGB leds[NUM_LEDS];

void setup() {
  // put your setup code here, to run once:
  FastLED.addLeds<WS2812, LED_PIN, GRB>(leds, NUM_LEDS);
  pinMode(buttonPin,  INPUT);
}

void loop() {
  // put your main code here, to run repeatedly:
  buttonState  = digitalRead(buttonPin);
  if  (buttonState  ==  HIGH) {
    leds[0] = CRGB(255, 0, 0);
    FastLED.show();
  }
  else  {
    leds[0] = CRGB(0, 0, 0);
    FastLED.show();
  }
}

How do you want the buttons to behave?
One button to move where you want to drop the game piece one column to the right (wrap around if they push the move button from the right most column).
Another button to drop the game piece.

Or do you want 2 move buttons, one for right and one for left.