Alluvial Gem Mining
This will work anywhere there is a deposit of gravel, or virtually anywhere you want to dig even in your own backyard. This does not mean that gemstones are common they're not, but your chances of finding a valuable gem is as good as not. The simplest form of alluvial gem mining is "Artisimal" mining. This was the type of mining depicted in the recent movie, "Blood Diamonds." Although in many places it has been modernized by using heavy equipment, and gravel processing machinery of many types in other places it is still being practiced the sane way it was in the bible.
The thing about doing this type of gem mining is how simple it is in practice. All you need for equipment is a shovel. This does most of the heavy work. From there you can get as exotic as you want although I will admit that a great deal of the other equipment you'll need is kitchen accessories. A plastic colander is probably your next most important tool. This acts as a sieve, and also as a device for concentrating the possible gems. This works on the simple premise that most gemstones are denser then the surrounding gravel. Being denser they will sink to the bottom if the colander is jigged up and down in water concentrating the heavier stones at the bottom. To get at any potential gems quickly turn the colander upside down on a flat surface this causes any gems to come out on the top of the heap.
I would suggest that you acquire a field book on gems and minerals so that you will be able to identify what you have found. In general what you are looking for is something that looks different from the surrounding gravel. This is usually something that is off colored. They can be any color of the rainbow. Generally, most rough gemstones are transparent, the more transparent they are the more valuable they are.
By jigging all you are doing is repeating the natural process by which nature concentrates any gem material at the bottom of the gravel load. To find most gems it is necessary to get as close to bedrock as possible because this is where the gems are. They are especially apt to be found in any natural basins that may be eroded into the bedrock, or any crevices. An especially good place to look is anywhere the speed of the currant drops off quickly. This is usually a good place to look for gold, or trout. Another good place to look is the plunge pool found at the bottom of a waterfall.
Do not think that exotic gems only come from far away, exotic countries because your own backyard is just as apt to produce a valuable gem for you; just go look. The stones that are really easy to find are members of the sapphire family. Remember this includes rubies the most valuable gem.
There are a number of companies that search for valuable gems on a commercial scale. One that comes to mind is Rockwell Diamonds Inc. of South Africa. They are hunting diamonds along the middle Orange River and have found several very large stones that are worth millions each. There are many others found throughout the world.
Good hunting, and good luck!