I often fill my pan pretty full, dunk the entire pan in the river and get everything fluid and turning the pan back and forth like using a steering wheel left and right. Gold is very heavy and will start to sink much faster than the other material just make sure everything is in suspension. Then the main aim is to start skimming layers from the top using water, don't be too rough at the beginning just gently make the water peel off the top soil and rocks, dunk more water in, shake and turn the pan again and repeat the process.
Within a few times of doing that, most of your gold will now be sitting on the bottom of the pan. BE PATIENT. While gold is heavy, you will rarely get big pieces and you need to continue the skimming until almost all of your soil/clay/pebbles are gone (maybe 2 tablespoons of soil left from a full pan)........you may think there's no gold in the pan and then all of a sudden you notice a spec or two sitting in the corner of the pan. If you can use your imagination try thinking where all the heavies should be....and they will probably be there. As Tom has indicated practicing with lead can be done at home and allows you to understand what heavy stuff does in the pan.
Once you have not much soil left you can do the "reveal"...the fun part in panning where you swish extremely gently normally anti clockwise and the gold stays put while the dirt swishes away with the water.
Everyone has their own panning method and they all work on the same principle. Don't feel shy about how you pan, we all do it different. Even if you use a classifier you may get some stones in your pan, just pick them out as required but make sure if its a heavy piece of rock in your pan, it may have some gold attached, and you can also find sapphires etc.
In Gold areas I have often found more near the surface than digging too deep....clay layers are often what has the gold sitting on top of that layer....poke around the river rocks and you see grey clay just under them after a bit of digging around, you will more than likely be finding gold soon! Good luck out there.