Summarize:

Take a full, long drag and keep the smoke in your mouth. Smoke rings only work with thick, fully formed smoke, so consider using a Hookah or cigar to practice. Some people have success pulling their lips back over their teeth, but the overall goal is simply as if you were saying "oh." Keep your mouth open and round and you'll be perfect. There are a lot of schools of thought about how to best accomplish this, as it is the hardest part of blowing rings: Exhale with rapid, clipped breaths. A lot of groups call these "reverse hiccups." A hiccup is basically a quick, brief inhalation. It feels almost like a pop.Think of making a "Huh, Huh, Huh," sound as you push air out. Use your tongue to "flick" out bits of airs. Time your flick with a puff of air, almost like a heavily enunciated "to." Tap out the rings. Contort your mouth so that your cheeks are concave (curving into your mouth). Tap the cheek with a finger, hitting it hard enough to force some air out of your mouth. You can tap rapidly as you get better and better. Rings are determined by the size of your mouth and the force you use to push the smoke out. Once you get the basic idea down, practice moving your lips and working your lungs to get different sized rings.. You can make your rings into little hearts easily. After you blow it out, snap just above the ring, 1-2" high. The resulting burst of air will dent the top of the ring, making a heart appear.
Get a full mouth of smoke. Open your mouth to an O shape. Use quick bursts of air to push the smoke out. Change your mouth shape to change the ring shape.