Based on raspberry pi tutorials and tested on the pi zero.
Use a standard led and 220 Ohm resistor.
The pin layout on the zero is the same as bigger models can be observed here:
import RPi.GPIO as GPIO
import time
GPIO.setmode(GPIO.BCM)
GPIO.setwarnings(False)
GPIO.setup(18,GPIO.OUT)
print "LED on"
GPIO.output(18,GPIO.HIGH)
time.sleep(1)
print "LED off"
GPIO.output(18,GPIO.LOW)
and run
sudo python LED.py