The key to blowing smoke rings is mostly
in the tongue. The tongue itself, is like a
piston, to draw massive amounts of smoke
into the mouth while the tongue is recoiling
to the back of the mouth. Keep the smoke
in the mouth, do not inhale to the lungs.
Next, open a large hole with your lips, full circle,
while not allowing the smoke to escape, holding
everything still.
Next, use the tongue to "pop" the smoke out and
quickly pull the tongue to the back of the mouth.
The tongue action is a quick push/pull back action
sort of like a viper attacking and quickly recoiling
for the next action, then hold, for the next ring,
when you are ready.
I usually push/pop/hold while the ring is drifting into
and out of existence before sending out another
ring, or when I am ready to blow a ring in a ring.
Now, once you master blowing your rings, the next
step is to try blowing a ring inside of a ring. You
simply need to wait until the first ring expands into
a larger circle, and once sufficient, to then blow a
second ring through the first. Keep in mind that you
can do this remaining exactly where you are since
the second ring, if blown hard enough, will reach the
first because the first will slow down eventually due to
entropy.
I hope this helps!