I regularly receive many inquiries from persons around the world who have questions about gems, gemcutting, and the like. Here is a representative sampling of the questions I get.
Check my links page for a few schools that offer correspondence and on-campus courses. Gemology is not taught at too many different institutions. GIA is the primary educator of gemologists in the U.S., but there are a few others scattered around the globe.
Real alexandrite has always been rare and expensive, especially in large clean stones. The likelihood of your finding one in the family jewels is on the order of winning the lottery; i.e., fat chance! Many thousands of inexpensive synthetic sapphires with an alexandrite-like color change have been sold as "alexandrite" for several decades, especially to tourists in resort areas. If you have serious reason to believe your stone is genuine, take it to a qualified gemologist/appraiser for identification. Be prepared to pay a reasonable fee for a professional examination.
It's always fun to go rockhounding and digging your own mineral specimens. Unfortunately, the vast majority of stones found by casual diggers are of very poor quality and not worth the cost of cutting, especially in the tourist "mines" around resort areas. If the stones look promising to you in terms of color, clarity, size, and shape, let a good gemcutter have a look at them. The preliminary examination is usually at no cost. Cutting costs vary a great deal; professional cutters in the U.S. often charge $30-40 per hour for cutting. Stones can be cut very inexpensively in various third world sweatshops, but it's often prohibitive to do this unless you're working with large numbers of stones and can wait several months for their return.
Opals are soft and like many other stones can become scratched and dull-looking over time. Usually they can be repolished at low cost with little or no weight loss. Show it to a good gemcutter for an expert opinion.
The internet has a growing number of good resources for subjects such as this. You can find a brief description of many stones on my "rainbow" page, and there are some links to other resources on my links page. Don't forget to try any of the popular search sites, such as Yahoo, Altavista, Excite, Infoseek, Lycos, and so on.
Read my investment page to learn about some of the pitfalls of "investing" in gemstones. Unfortunately, it can be very difficult for the average person to sell such gemstones. Recently, internet auction sites such as Ebay have provided a possible outlet for this sort of activity, but quite often gemstone investments turn out to be big money losers. Caveat emptor!
Traditionally, only stones such as diamond, ruby, sapphire, and emerald were considered precious. However, the terms are essentially meaningless now, and "semiprecious" sounds to me a lot like "semiworthless." One can easily find low quality diamonds, rubies, sapphires, and emeralds that are worth pennies per carat, and so-called "semiprecious" stones such as garnet and tourmaline can easily be worth thousands of dollars per carat (as in tsavorite garnet and Paraiba tourmaline). It makes much more sense to refer to the various gemstones by name and quality.
All gemstones, even diamonds, are relatively fragile and can be damaged by a hard blow, by a jeweler's slip during stone setting, by rubbing against other gemstones in a jewelry box, etc. In many cases, they can be recut and repolished with only minor weight loss. Show your damaged stone to a good gemcutter for an expert opinion.
It's frequently, or perhaps usually, impossible to identify a gemstone on the basis of a photograph. Many different stones closely resemble each other and can only be positively identified through gemological techniques such as microscopic examination of inclusions, measurements of refractive index, and the use of other gemological tools and techniques. Also, after the stone is identified, it make take a qualified gemologist/appraiser to evaluate the stone's quality and determine an appropriate value. Appraisals often tend to be worth what you pay for them -- don't expect a professional to offer an expert opinion for free. He/she worked long and hard to obtain specialized knowledge and should not be expected to give away the results of that hard work gratis.
Sorry. Good lapidary equipment has a way of being snatched up as soon as it becomes available. Your best bet may be the classified ads in publications such as Lapidary Journal or Rock & Gem, both of which are available at most newsstands.