In theory, you pan in the creek at the likely spots where gold might be found and continue to move upstream until you stop finding it. Then, you take dirt from a little up the hill on either side and pan that to find out which side it’s coming from. You might try panning first from the surface and also digging down several inches at a time and panning that dirt to make sure you don’t miss anything. Assuming you find something then you keep going up the hill doing the same and sampling left and right until the gold disappears and the highest up point on the hill where you find it should be near or at the source. When people are saying to dig they mean dig and then pan. You will never just dig through the first and expect to see gold. The idea is that if there is gold, there will probably be a fair amount of very fine gold that will more or less evenly distribute itself through the dirt/gravel on its way down to the bottom of the creek. This is what makes it possible to pick up the trace. Even if there are nuggets, you are unlikely to stumble upon one.
At this point you need to be keeping your eye out for expose outcrops of rock that looks like it might be gold-bearing and try to visually locate the source. If it’s completely buried then you have to keep zeroing in using the pan sampling method.
Have you read All gold canyon yet by Jack London? This describes the process as well but it’s also idealized.
In the real world, I don’t know how people have been successful with this method because there are so many variables that can throw you off. You will only be able to find the last gold source on the creek so you better start far up at the head practically. Unless there’s one vein in the area that is throwing off significantly more than any other, it will confuse your samples because you will be looking for very small amounts of gold in your pan. Creeks concentrate and strip gold in different areas and small creeks can be very random in this way so you may not find gold in a pan when you are still below the source. The same goes for on the hillside. You don’t know how well the gold will be distributed and at what layer in the soil it might be present. Vegetation and the shape of the hill will also affect how it moves. It might be more productive to just look for rocks that are likely breaking off a vein and follow those up. Depending on the steepness of the hill and the climate there might be none to several feet of first covering the bedrock where the gold is eroding from. Gold often is coming off a vein and not a point source and you may not know what direction the vein is running or if it is in the bottom of the creek itself. These are all just some thoughts but if you make some assumptions then you can come up with a decent story.
The last thing I would mention is that if this is to take place in the Dakotas most of those states would have practically 0 chance of having an original source of gold because it’s all just sedimentary rock and eroded soil. Any gold present would be randomly distributed through the sediment but it probably came from Canada or somewhere else long ago moved by glaciers or rivers. In the black hills and other mountains, the gold is found in the rock because there was essentially some volcanic activity underground that deposited minerals along with the rock.
