Gemstones have been sought after and treasured throughout history. They have been found in ruins dating several thousand years. They are valued as gifts symbolizing love.
Generally, the price of any gemstone is determined by: size, cut, quality (color/clarity/treatments), and type. Here are some questions to ask about quality:

Has it been treated?

Is the stone natural or synthetic?

Are there any noticeable scratches, chips or inclusions?

Is the color even throughout the stone?

How good is the color? (Is it vivid?)

If you are buying the stones for earrings or cufflinks, are the stones well matched?
There are many ways that dealers treat gemstones. The savvy buyer asks lots of questions and hopefully tests the results. Here are some treatments to look for:
Irradiation: It is common to irradiate Aquamarine, London Blue Topaz, Emerald, and Diamond as well as other stones. This treatment brings out color and removes imperfections. Many dealers know if the stones they are selling have been irradiated. Honest ones will tell you if they are aware of the treatment.
Heat Treatment: Amethyst, Aquamarine, Ruby, Tanzanite and Topaz are often heated at high temperatures to enhance color.
Dye: This is the most common treatment used. On clear stones, dye may be visible in cracks that are darker than the rest of the stone. Sometimes dye appears as a residue that rubs off or white patches. Lapis and Rose Quartz are commonly dyed. Amethyst and Citrine are often dyed. Black Onyx is permanently dyed in normal processing.
Coatings: Jasper is often dipped in petroleum products to bring out color and to seal it. Emerald is oiled; turquoise is waxed.
Fake stones: Some dealers will try passing off fake stones instead of natural ones. There are fake stones for most gemstones on the market. Always ask what stone something is if you are not certain. Honest dealers will tell you. If a stone looks too perfect it may be fake, irradiated or dyed. I avoid Laboratory made products are known as synthetics.
Tips on buying beads:
Good sized holes (so can use a stronger thread)
Evenly shaped beads (as appropriate)
If the beads are being sold in a 16" strand -- I make sure it is 16" -- not 14" or 15" if possible.
Look for the best quality stone (if buying real stones)
Make sure beads are not cracked or chipped by the holes as this tears the thread
Good color (so can create harmonious necklaces and matching earrings)