Haha I don't think there is any "fool proof" way, but I can give you some pointers! I learned on hookah, which is probably the best way to learn because the smoke is so dense and steamy. But it works with a pipe too.
First just get the pipe burnin' hot so you can get a really dense smoke, then take in a healthy serving of smoke. Try to make somewhat of a circle with your lips (starting smaller is easier) and then push small burst of air out of your lungs. The less air you can push out the better, people usually blow way to hard. This is going to be hard to explain, but what you want to do very briefly open the back of your mouth and close it. It will make an "ah" sound with a little click (only audible to you). Then it just happens! Otherwise if pushing the air out is too tricky, just get a bunch of smoke in your mouth and flick the side of your cheek!
Other tricks are double smoke rings, just lay you index finger across your lips in the middle and do the steps to a normal smoke ring and often two rings will come out in either directions. You can french inhale. You can catch clouds (blow a condensed ball of smoke just outside your mouth, let it linger, then suck it back in). And if you get a toilet paper roll and some dish soap you can blow smoke bubbles! haha
Best of luck!