The biggest factor in blowing good smoke rings is practice. With that in mind, Try this technique.
First, you need a cigar with dense smoke, and a place with still air. Do not waste your time trying to blow smoke rings in a breeze!
Draw a thick puff of smoke into your mouth. Hold it there and open your mouth slowly. Make an "O" with your mouth, (maybe more of a rounded "oh"), definitely not a pucker like a kiss. Curl the tip of your tongue down, and pull your tongue all the way back.
Now, when blowing a ring, you are actually not exhaling. You are just pushing out the smoke in your mouth with your tongue in short bursts, like a piston, only in a relaxed way. It is actually a really gentle motion. Push forward with your tongue, with perhaps a slight recoil at the bottom.
Keep at it, it is like riding a bicycle... Once you "get it" you will wonder what the problem was!