Converting a standard setup/loop sketch to a low power application?
This sketch is almost identical to the powerDownWakeExternalInterrupt.ino sketch that comes with the LowPower Library. I'm using INPUT_PULLUP and a N.O. push button switch to trigger it to wake up and turn an LED on.

#include "LowPower.h"
const byte wakeUpPin = 2;

// Just a handler for the pin interrupt.
void wakeUp(){}

void setup(){

  // Configure wake up pin as input.
  // This will consumes few uA of current.
  pinMode(wakeUpPin, INPUT_PULLUP);
  pinMode(LED_BUILTIN, OUTPUT);
  digitalWrite(LED_BUILTIN, LOW);

}

void loop(){

  // Allow wake up pin to trigger interrupt on low.
  attachInterrupt(0, wakeUp, LOW);

  // Enter power down state with ADC and BOD module disabled.
  // Wake up when wake up pin is low.
  LowPower.powerDown(SLEEP_FOREVER, ADC_OFF, BOD_OFF);

  // Disable external pin interrupt on wake up pin.
  detachInterrupt(0); 

  // Do something here.
  digitalWrite(LED_BUILTIN, HIGH);
  delay(2000);
  digitalWrite(LED_BUILTIN, LOW);

}