LED (Example)   Hardware

Equipments
1. Raspberry Pi
2. LED
3. Resistor 220 Ω 
Using PWM in RPi.GPIO
To create a PWM instance:
p = GPIO.PWM(channel, frequency)
To start PWM:
p.start(dc)   # where dc is the duty cycle (0.0 <= dc <= 100.0)
To change the frequency:
p.ChangeFrequency(freq)   # where freq is the new frequency in Hz
To change the duty cycle:
p.ChangeDutyCycle(dc)  # where 0.0 <= dc <= 100.0
To stop PWM:
p.stop()
Note that PWM will also stop if the instance variable 'p' goes out of scope.
An example to blink an LED once every two seconds:
import RPi.GPIO as GPIO
GPIO.setmode(GPIO.BOARD)
GPIO.setup(12, GPIO.OUT)

p = GPIO.PWM(12, 0.5)
p.start(1)
input('Press return to stop:')   # use raw_input for Python 2
p.stop()
GPIO.cleanup()
An example to brighten/dim an LED:
import time
import RPi.GPIO as GPIO
GPIO.setmode(GPIO.BOARD)
PWMPin = 12 # or any GPIO Pin
GPIO.setup(PWMPin, GPIO.OUT)

p = GPIO.PWM(PWMPin, 50)  # channel=12 frequency=50Hz
p.start(0)
try:
    while 1:
        for dc in range(0, 101, 5):
            p.ChangeDutyCycle(dc)
            time.sleep(0.1)
        for dc in range(100, -1, -5):
            p.ChangeDutyCycle(dc)
            time.sleep(0.1)
except KeyboardInterrupt:
    pass
p.stop()
GPIO.cleanup()