Veteran smokers note that in order to blow a good smoke ring, you will need to create dense smoke. Draw a deep, dense smoke puff into your mouth. Hold the smoke there and then open your mouth slowly and deliberately. Open your mouth, shaping your lips into a rounded 'O.' and pull your tongue back as you expel the smoke.
Keep in mind that you are not exhaling the smoke, but simply pushing it out of your mouth. Also keep in mind that this maneuver will not work if there is even a slight breeze in the air. Make sure you try it in a location with still calm air. Just like everything else in life, practice makes perfect.