Cabochons.biz 
Cabochons.biz This is known as orientation.
Try to select the most aesthetically pleasing rough , remember to orient the rough for finished symmetry, angle of view once cut. Then we must strengthen the back before cutting. it may be best to lightly pre form and lightly slice or trim your selected rough.
Here is are examples of selection from Demale mine rough,
This is our teaching stone rough for this example. 
Here is a cutting machine
used primarily for cabochon cut. I can recommend the Diamond Pacific,
"Pixie" machine, shown however other less expensive lapidary cutting
options are widely available.
When I first began many years ago by using sandpaper in varied grits from very coarse and working to very fine grits once the primary shape was established. Next buffing with a simple rotary tool and chemise buff with cerium oxide polish paste made from mixing cerium oxide with a touch of water stirred into paste.
Now there are very fine quality sandpaper sponges available that would allow a very patient new cutter to begin. (See Rio Grande Catalog) Also there are some lesser priced machines, however I recommend the drum style cutting wheels that are pre charged or embedded with corundum. Avoid the flat cutting lap styles for cabochon cutting, these are best for faceting or merely doing the underside of the cabochon and you will not require them.
Another good "Po Boy" style "Cabber" I used long ago in a friends small island jewelry shop, that worked surprisingly well, was a worn out sandpaper belt set up that offered enough slack to make it flexible for shaping your cabochons. Then a polisher. If you look or are creative it there are many easy ways to begin cutting on a budget, so almost anyone can obtain some rough and give this fun occupation a try.
Turquoise rough gem can be very brittle in nature, often it occurs thinly and with the lovely matrix spider webs we all love and admire.
Choosing the right piece of rough to cut and how you decide to orient the cut of your cabochon is a key factor that will involve a bit of thought and observation as to make the most from the rough you have.
Challenges abound , such as considerations for the strength of host rock or matrix during cutting , this host rock where the formation occurred is what makes up the webbing that forms in and around frequently in turquoise, adding character, appeal and value.
Webbing patterns that we so love, usually leave the Turquoise vulnerable by nature to separation
along these beautiful patterned lines, this means as it is being cut for you it
is very likely to fracture or fall apart.
Internal weakness may be undetectable to the naked eye, often causing your stone to literally come apart and even disintegrate while you are cutting , or cause the finished gem to be too fragile for everyday wear. Others develop fractures soon after cutting or setting of the stone.
* This is why ! .., We need to back our turquoise before cutting and
polishing.
Observe below the picture of the bottom (or back of cab') from a lovely Kingman mine cabochon (shown above,) it was cut without any backing from the rough it is leaning against. It took very only very light pressure to cause it to break as seen above.
It has been coated with clear and sacrificed for this demonstration to show you the many areas of matrix that lend more vulnerability to an already brittle gem.
What products are suited to backing turquoise?
Many ways and products do exist and can be used. Ones that may shrink as they cure should be avoided however.
Durable 2 part steel weld epoxy loaded with metal is the preferred old favorite for experienced turquoise lapidary professionals.
* Note the metal in the 2 part glue eventually does show rust if examined after some time of wear or exposure to water. While few lapidaries address that "Future" problem, and leave it as ready to set, I have adopted a technique for either clear coating the BACKING only to prevent the eventual rust. Alternately on finer gems I solid gold or copper leaf these to denote rarity and value in finer or rare items of added value.
Even hard flat items cut to fit and glued on have been used for adding strength, be it old car battery plastic or even harder stone, many things have been tried and tested.
For this
example a 2 part weld epoxy has been used.
Here the weld epoxy has been spread evenly less than a quarter inch thick to the underside of the rough we intend to cut. Prepare these 24 hours in advance. Next using a "Dop Stick" and lapidary "Dop Wax" you will affix the prepared rough to the layer of epoxy backing. Then you can safely proceed to cut your turquoise with minimal risk. REMEMBER: Take care always to look allot and grind a little as you cut.
Now you are ready
to "Dop" your new gemstone creation to cut shape and polish it safely,
without fear of cracking in most cases. (See next picture.)
The new backing has added
much more stability, strength and safety for both cutting and future setting and
wear.
With practice there should be very little chance of it being damaged in the processes of cutting and polishing.
Also do not let your turquoise become hot while cutting, especially if you are not able to be using a coolant. Always.... "Cut a little & look allot." As it is VERY easy to remove to much gem rough material while cutting a new Cabochon, and if you over cut even a little there is no way to replace it.
* If for some reason your cutting set up is not using a coolant, you should consider having a non food use bowl filled with water to frequently dip the stone in as you cut and shape your new cabochon.
Cut and polish while attached to a simple "Dop" stick
with dop wax as
shown. Seat your gemstone firmly with dop wax in between the bottom of your
stone and the small short stick used as your dop stick Any small evenly cut
dowel will suffice as a dopping stick.
After cutting from your coarsest grit and shaping , we work our way gradually to finer and finer grits according to what we have for our set up.
Common cutting grit values and order for turquoise or opal , is as follows:
A.) 80 grit wheel, Used primarily to clean & prepare the host rock gently if need on rough with lots of excessive host matrix.
B.) 220 grit wheel, A finer grade Used much as above either as your next step or a rough shaping grit to begin your cut.
C.) 380 grit wheel, Again your next finer grade when starting from turquoise with host rock. OR
NOTE * If beginning with pure backed turquoise 380 is a proper Starting grit.
D.) 600 grit Is The next logical grit step. * Also it is where some lapidaries finish cutting and go to polish.
E.) 1,200 grit Is next, and a safe grit to finish at for a decent project.
F.) 14,000 grit wheel is where finer quality products such as gem grades should at least go to, so that you obtain a highly smooth natural polish from the cut.
G.) 50,000.or 100,000. Diamond Grit, comes in Pastes, Polish on a leather wheel with 50,000.-100,000. DIAMOND PASTES: You can order these directly, in an easy to use syringe. These are excellent to seal the gemstone naturally as well. (Again see Rio Grande's catalog.)
H) Finish Buff, I use a half horse power buffer with Fabulustre brand polish after 100,000. Grit diamond polish on a worn leather lap. A step that also helps seal your new gemstone. (This polish should be available through Rio Grande, it is good on these "Softer" Gemstones.)
NEXT: To free your gemstone from the Dop wax and stick after you complete your final polish, use the *old faceter's trick below.
* Simply take your newly cut gemstone, while it is still attached to your "Dop Stick," and place it very carefully in your freezer, so that the wax then becomes brittle. Next: Let your new gemstone sit for about 15 minutes or so, after witch it should gently separate from the wax and stick with merely a delicate lift. *If it takes any pressure at all to lift it clean and free place it back for a few more minutes and try again. We do not ever want to rush in gemstone cutting and polishing work.
While it is not essential, once you have a sturdy completed gemstone, now you may want to aesthetically touch up the backing.
I myself have taken to adding layers of pure gold or copper leaf to indicate the more valuable cabochons from the average commercial grade. This just adds a bit of appeal by dressing it up a bit. Available at places like Rio Grande from Mr. Bell's family.
This simple addition also to me signifies a proper acknowledgment to quality, rarity, and value of the gem at a glance.
Finished Cabochon , AFTER: 
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