When I think of backyard geology, the first thing that comes to mind is gold. Of course, it's not in everyone's backyard, but it can be found. There's an old saying, "gold is where you find it"; in other words, look for gold where it's already been found. I'm not sure I agree with this.
I live in the foothills of the Appalachians and, supposedly, our mountains weren't "pushed" high enough out of the earth to expose gold deposits. Yet, only a few hours away, in Dahlonegah, Georgia was one of the largest gold finds in history. You can still mine for gold over there if you know someone with a nice little stream.
About three hours south of where I live is Talladega National Forest. There are plenty of old gold mines there, as well. I have done some panning in this area and came up with some "color". It's exiting!
What you need to find is a nice lazy stream that goes wild during the rainy season. You don't want one that is a mud hole or always flows slowly. When the water is gushing gold, a very heavy element, is pushed downstream and hopefully trapped in several different places.
Where to look in the stream bed:
Find larger boulders that you can move fairly easily and you just might find a nugget wedged underneath or on the downstream side of the boulder itself, and where it lay.
Look for mossy areas on old logs or rocks. Go through them easily with your fingers, looking for that flicker of gold. After you have gone through the moss; easily move the limb or log or boulder and see if luck is with you.
Don't forget the creek bank! During the rainy season, when the stream is raging, it very well could deposit gold in "pockets" along the side of the creek bank. Look there for mossy areas, and deposits of rock, sticks and logs.
Finally, take out the old gold pan. If you see black sand, work it in your pan. Usually where there is black sand, there is gold. After you have panned the water and sand out of the pan, the heavier gold remains a beautiful, shiny yellow on the bottom of the pan. You need a "snuffer" bottle; a plastic bottle with a pointed top with a hole in it. Gently "snuff" or "sniff" the placer gold (gold findings that are specks in stream beds) into your bottle. While you are going through these steps, watch for quartz crystals, too. They could indicate the presence of gold.
Beware of iron pyrite, or "fools gold". It is rather flashy, but should stick to a small magnet. Get out there and prospect...if you find it...it's there!