I do a lot of Clinton Anderson type excercises where I get the horse to move away from the pressure of the my body.
So that being said, I stand in a halter showing position next to my horse. Turn with my feet facing the way I want to go while being far enough in front of my horse's shoulder so that I am looking him dead in the eye.
I walk in a big circle staring at his eye and pushing his eye away from me. I will back this up with the CA method of moving him off of my presence - be it flicking my hands and hissing or pushing with my thumb at the junction of his neck/shoulder or thumb pressing jaw near the halter. Goal being to release the pressure as soon as he moves off so eventually he will move when I turn my feet and lean my shoulders and hands forward to go.
The pivot is forward motion and his front inside foot (closest to you) should cross over the outside foot, the outside hind foot (which will actually be the center of the circle) will mostly stay in one place.
You yourself have to walk in a big enough circle to give the horse room to turn.
So work on getting him to give to pressure - I personally get the walk/trot/stop in hand, disengaging of the hindquarters, and backing down first before pivoting. And work on your postion so that you give him room.
Here are a couple of pics of me teaching my filly.