most of the people i know do the pop/snap jaw method.

the way this method works i believe is that once your lips are in an O shape. the quick and remember 'slight' pop/snap of your jaw, increases the air pressure in your mouth thus pushing the smoke out but the reversal movement that comes with the pop/snap quickly decreases the pressure almost immediately after, which shapes the smoke into that O shape as it's leaving your lips.

Practice in front of a mirror. thats how i learned.

and heres a way to blow heaps of rings with no skill but just for fun. take a drag of your cigarette, do not inhale the smoke. keep it in your mouth. now make an O shape with your lips. you don't need to breathe out for this method. hold your breath.

now with the smoke in your mouth and your lips in an O shape, take a finger of yours and tap your cheeks lgihtly and repeatedly, smoke rings will start to pop out of your mouth in rapid succession.