Obtain a day pass to pan at the Black Hills tourist facility at which you intend to pan. Many places will let you pay a single price for your day of panning and let you keep all that you find in the day, regardless of the total price of nuggets that you find. Purchase or rent a pan from this facility or bring your own.
Dig a load of rock, sand, and clay out of dry land or from the middle of a stream and place it into your pan. Place no more than an inch deep layer of ore and dirt along the bottom of the pan so that you do not spill the contents of your pan while you are panning.
Fill the pan halfway with water and begin working the pan back and forth in a side-to-side motion. This motion will make the heavier particles in the pan fall to the bottom, which is exactly what you want because gold is heavier than grains of sand and other rocks. Work the rocks over with your hands to bust up clumps of dirt and clay.
Tilt the pan underwater, completely submerging it in a gently moving stream. Tilt only enough to remove the lighter materials on top of the pan. Make sure the heavier materials stay in.
Repeat the above steps until nearly all the lighter material is removed from the pan. Pick the larger pieces of rock out from the bottom of the pan and take a look at the gold dust and nuggets in the bottom of your pan.