how to test to authenticate a gem stone

Yes and no. For some materials, though not all, the handheld devices can help separate stone from glass. At best, they can provide one piece of evidence in the process of narrowing down what you have. I am assuming that you are referring to reflectivity meters and/or thermal probes, but the same comment holds true for any individual piece of equipment.

For faceted or flat-polished stones, a refractometer narrows down things greatly. Reflectometers are a bit less accurate, but have the advantage of being more portable. A specific gravity (SG) setup is also a great piece of equipment to have (or make your own). Other simple equipment such as a dichroscope, filters, microscope, etc. can come in handy to narrow things down further. Unfortunately, an all-in-one piece of equipment to identify a stone has yet to be invented (although some of the super-expensive lab machines come close).

Then, after you've narrowed down what you have, you start looking and testing for signs of treatments such as coloring and filling or synthetic/artificial to finish up the ID and disclosure. I would love to have Mr. Spock's Tricorder, or at least something portable that would do a safe Raman scan.

Thanks for the mention Scott but it appears to me that rocks2dust analyzed the problem very well. Gem ID is not a simple matter, especially when modern methods of gem treatment and synthesis are considered. I own a reflectometer and in my opinion it's completely unreliable. I've noticed some sellers are now calling them digital refractometers which is very misleading. They still measure reflectivity which varies a lot depending on the quality of polish, cleanliness of the stone, machine calibration etc. Also, many of the cheap Asian-made optical refractomers tested by expert gemologists are considered unreliable. Unfortunately quality gemological refractometers start in the $500+ range and go up a lot from there.

Rocks2dust mentioned making your own testing equipment and it's a good idea. Dr. William Hanneman's "Guide to Affordable Gemology" is said to be available in a new printing at www.mineralab.com/Gemology.htm  It contains basic gemology information plus instructions for making some essential instruments very inexpensively.

There's actually a fairly simple way to ID transparent gems that requires only a penlight, tweezers, and an educated brain/eyeball combo. It's called the Hodgkinson Method (aka Visual Optics) after Scottish gemologist Alan Hodgkinson who systematized it. Getting maximum use from it requires considerable memorization and practice but learning just a few simple procedures can be very helpful: Rubies and garnets can be differentiated in seconds (but not whether the ruby is synthetic!) With a little practice I've found it's easy to tell diamonds from CZ, Moissanite and other transparent white gems. Unfortunately Hodgkinson's book, "Visual Optics - Gem Identification Without Instruments," is out of print.

This link gives the general gist of how it works: www.cigem.ca/411.html

I am with gemfellar on this .. you can train the eye .. but you need to look at alot of stone"S ! all them machines can be expensive and still you need them all .. not just one !