Display the handkerchief to the audience to show that it is normal (because it is). Hold it by two corners so it hangs down and display both sides. This effect is easier to accomplish with a larger piece of cloth, so a woman's scarf works even better than a normal handkerchief. When magicians talk to each other, they like to call handkerchiefs "silks," even if they are not silk and larger pieces of cloth are "foulards."
Tap the wand against something to prove it is solid. Pass it out for examination if there is time to kill, but try not to drag this out. It really is not worth it. Part of being a good performer is pacing effects correctly.
Extend the left hand and make a fist with the thumb up. Magicians call this "holding out the left fist." Cover the fist with the foulard. It is best to place the foulard so that one corner is draped in front, one on each side and the fourth corner along the left forearm. This is important so pay attention. The center of the foulard should be about at the left wrist, not on top of the fist.
Poke the foulard slightly into the fist with a finger or the end of the wand. Pull the corner of the handkerchief back over the left arm and draw the audience's attention to the fact that the cloth is pushed into the fist and the fist is closed. This really is not important at all, but it sets up the next move, which is literally where the magic is going to happen.
Grab both corners resting on the left arm and pull them over the front. Instead of the front corner hanging in front of the left hand in the audience's view, it is the corner that was on the left arm. DO NOT draw the audience's attention to this. It leaves part of the left hand, basically where the thumb joins the hand, exposed.
Slide the wand between the thumb and the foulard (still not cool); drop it, and let it fall through. Repeat quickly if desired and immediately drop the foulard, catching it by the corners to again display it and prove there is no hole, door or trickery of any kind.
Return any borrowed items. Consider performing another effect, but do not try the audience's patience. When in doubt, bow and leave.