How can I make push buttons react to being pressed instantly? I am making an Arduino alarm clock. I am checking for the state of a button. If it is clicked, I increment the button counter. If the counter is divisible by 2, it is mode 0, if not, it is mode 1. I have small delays in the code for each mode to help the lcd clear itself. Those delays are preventing the buttons to reacting to my touch, because there is likely a delay during that time. 

#include &lt;LiquidCrystal.h&gt;
LiquidCrystal lcd(12, 11, 5, 4, 3, 2);
int hours=0;
int minutes=0;
const int modePin=6; //button
int prevModeState=0; //prev state of button
unsigned long timer;
int modeState;//current state
int mode=0;//mode of alarm
int buttonCounter=0;
void setup() {
lcd.begin(16, 2);
lcd.setCursor(6, 0);
lcd.print("Time:");
lcd.setCursor(6, 1);
lcd.print("00:00");
pinMode(modePin, INPUT);
}

void loop() {
modeState=digitalRead(modePin);
if(prevModeState!=modeState){    //this is the part where I check for the state
  if(modeState==HIGH){
    buttonCounter++;
  } 
}
prevModeState=modeState;
if(buttonCounter%2==0){
  mode=0;
}
else{
  mode=1;
}


if(mode==0){
  timer=millis();
  if(timer%600==0){
     minutes++;
    if(minutes==60){
        minutes=0;
        hours++;
        }
     if(hours==24){
        hours=0;
     }
    lcd.clear();
    lcd.setCursor(6, 0);
    lcd.print("Time:");
    lcd.setCursor(6, 1);
    writeTime();
    delay(200); //delay
    }
}
else if(mode==1){
  lcd.clear();
  lcd.setCursor(4, 0);
  lcd.print("Set Time:");
  lcd.setCursor(6, 1);
  writeTime();
  delay(500); //delays

}
}

void writeTime(){
if(minutes&lt;10){

      if(hours&lt;10){
        lcd.print(String("0")+hours+":"+"0"+minutes);
      }
      else{
        lcd.print(hours+String(":")+"0"+minutes);
      }
    }
    else{
      if(hours&lt;10){
         lcd.print(String("0")+hours+":"+minutes);
      }
      else{
         lcd.print(hours+String(":")+minutes);//possibly split if problems arise
      }

    }
}


How can I edit my code?
You have a few options, including using interrupts. But I believe the most important thing is: "do not use delay()" and you might not even need to use interrupts...

Have a look on this nice post from Nick Gammon: http://www.gammon.com.au/blink with some tips about non-blocking coding.

Also a very simple "Blink LED" example: https://www.arduino.cc/en/Tutorial/BlinkWithoutDelay