For me, I teach my horses this way... and like GotaDun said, it's a lot harder to explain than do, so bear with me.
First, it is a forward motion. Pay attention to his fronts and make sure he steps the left knee over in front of the right, not behind. His back right is the correct pivot.
So, when I start my horses I put myself in the correct position. I stand beside her, my shoulder to her upper neck, facing forward with my body tall and my neck straight and tall, chin up. My elbow at a 90 degree and my hand holding my lead with a slight dip in the chain.
I walk forward, then drop my shoulders back (more obvious at first, then more and more subtle) to stop .. give a low, deep WHOA. (Eventually you wont need to say WHOA, they will go off your body cues).
Turn and face the horses head, and To teach the first crossovers -
Raise your hand up and back slightly, the goal is to rock him back on his hindquarters, so his weight makes it more difficult to get that back right off the ground. Then walk slightly forward and into his nose... this is the tricky to write down part, because you want to go forward enough that the front legs cross correctly, but not too far forward that you walk him out of the setup.
If you get a step or two with him crossing the fronts correctly, walk him out of it and praise him. Do this every day, increasing the number of correct steps. If you get the fronts crossing correctly, you will notice the right hind stays stationary while the hind left crosses in front of it.
After a week or two you should be able to pivot 1/4 turn pretty easily - so walk him forward, turn sharply (but smoothly) into his face, cluck for the pivot, get the 1/4 turn, walk forward about 10 feet and repeat until you formed a square (4 1/4 pivots)
When he gets this down, up it to a 1/2 pivot.
Then when he gets that, up to a full pivot.
If you don't rush and get frustrated, it will go much quicker and he will be a better showmanship horse. Let him get confident.
Hope that helps...
There is no passion to be found playing small - in settling for a life that is less than the one you are capable of living. - Nelson Mandela