How does a rough piece of rock become a gemstone? The following description and pictures show and tell how one piece of rough became a finished stone
1. Selecting the rough: For this little narrative I'm simply looking for a clean piece of garnet rough that will be cut into a standard round brilliant (SRB) cut. I want a clean stone that's well shaped to minimize loss so I'm looking for something that's fairly rounded, and shows no obvious cracks or inclusions when sidelit with a penlight.
We have a winner! Nice color, not too dark and it should yield a finished stone of over 1 carat. Original rough weight is 4 carats.
2. Cutting the table: Using a 1200 grit diamond lap, I'll grind a flat spot to give me a place ot initially mount the stone on a keyed dop stick.
3. Dopping the stone: I like to use a specific  super-glue to hold my stones on the dop stick while cutting. They're not all created equal. Once the initial hold has take place, the dopped stone will sit 4 or more hours before I'll attempt any grinding
4. A little about the machine: The toothed wheel is called the index. The one shown has 96 teeth, so it's a 96 tooth index. These also come in other numbers depending on the number of teeth and are used for different cuts but the 96 is pretty much an industry standard, used in about 95% of the cuts that are out there. It's function is to provide repeatable rotational spots as you cut the stone, ie, on an SRB, the mains are cut at 96, 12, 24,48 etc. until you've done a full rotation on the stone
The protractor is used to adjust the angle of the cut and again, provides a repeatable reference as you cut. In addition, every gemstone has an optimum set of angles for light return and dispersion or fire. Too shallow and you wind up with a windowed stone that you can read through. Too steep and you'll wind up with a black hole it the stone. Right now I have the angle set for the break facets which I'll be cutting first
Last of all there's elevation. The wheel underneath the platform controls the height at which I'm cutting. It raises and lowers the platform without changing the angle on the handpiece. The black mark on the side of the platform is a reference mark I put there so I cand set the handpiece in the same spot after I lift it up to inspect the stone during cutting.
OK! It's cuttin' time! My first cut is to hog the stone out into it's intended shape. Here, I'm using a 360 grit diamond lap to cut in the "break" facets. These are the triangular cuts that will go underneath the girdle, or the edge of the stone. There are 16 breaks on the pavillion of an SRB. The angle here is  41 degrees with the index settings at 2-10-14-22-26-34-38-46-50-58-62-70-74-82-86 and 94. This is a rough cut just to establish the shape so I'm not pushing for high precision at this point.
Roughed in. The uncut part at the tip in no problem as it will close up when I'm putting a finer cut on the stone or when I cut the pavillion main facets
I've changed the angle to 90 degrees for cutting in the 16 girdle facets and will use the same index srttings as the breaks. Note the position of the left rear leg on the handpiece. I'm still using that mark as my reference point. A little side note here, many of the machines that are on the market come with depth gauges, and digital readouts that will split the angles to as little as 1/100th  of a degree of arc. The Raytech/Shaw clibrates to 1/10th and I do not use anything other than my ear and the sound the stone makes as it's cutting to tell me the right depth of cut. A cutting machine is a tool so the quality of cutting is highly dependant on how well the cutter "knows" his machine. The Raytech in this section and I have been buddies for about 20 odd years now so I can feel and hear the cut as it's happening. Yes I've worked with many other machines in the past but I always came back to my faithful Raytech/Shaw.
Cutting the girdle facets. Here I've switched laps and am using a finer, 1200 grit diamond lap to cut in the girdles. Again, I'm cutting by ear now to make the cuts all of the same depth.
The girdles are now cut in. Note the difference in finish between the side of the stone, where I cut using a 1200 grit, and the pavillion (the pointy end :)) where I used a 360 grit.
Here I'm going over the girdle facets with a lap called a NuBond. This is a 1200 grit diamond lap that, although it cuts very slowly, will give a much finer surface to the facets. 
Polishing time! This is where it really happens to the stone. Without a good polish the stone will lose it's brilliance. I tell student faceters that " Polish is evrything! Your facets may not align correctly, your angle may be a snidge off but it the stone's got a great polish it will still flash". Here I'm using a tin lap that's charged with aluminum oxide to put the final polish on the girdles. Another side note. For my first few years in cutting I didn't polish the girdles. After all, they're just little ones, right? Wrongo! Although they're small, they let a lot of light into the stone. Polished girdles considerable brighten the finished stone!
Ok, the girdle's polished. Now back to the break facets to even them up and lay a good polish on them.
The first step on the breaks is to even them up with the girdle so I have the corner of each break meeting up with the corner of each girdle. They'll also have to come to a near perfect center point at the tip of the pavillion. This is the first cut on them with the 1200 grit lap.
Repeating the breaks facets with the NuBond. Eack time I go over these cuts it leaves a finer finish on the surface of the stone. Also the rate of cutting slows so I can come as close to making the meet points as perfect as possible.
The break facets finished with the 1200 lap.
Here's one of the best laps to come on the market in a loooong time. This is a darkwing lap made by Jon Rolfe, of the Batt lap fame. The outside ring is charged with 5000 grit diamond while the inside holds an aluminum oxide charge. Right now, I'm applying the final prepolis to the break facets with the 5000 grit section, then I'll wipe the stone clean so as not to contaminate the inner part and go directly to the final polish. Thanks Jon :)!
Final polish on the inside ring of the Darkwing lap. Btw, check out my equipment pages in the near future. I'll be listing the Batt products there as soon as I get the time to make the update. Until then, if you're in need of any of Jon's great products give me a holler on the "Contacts" page.
The break facets are now done! Now on to the 8 mains or as they're sometimes referred to, kite facets.
Pavillion main time! I've adjusted the angle on the faceting head to 38 degrees and set the index wheel to 96. The mains will start out as a kite shaped facet on the tip of the stone and, as I lower the elevation on the platform, will seem to walk down from the tip until they're just above the girdle. I'll  walk them until they just touch the girdle when I polish them in. Index settings for the pavillion mains are 96-12-24-36-48-60- 72 and 84.
Cutting the pavillion mains. I'm starting out with the Nubond 1200 lap. There's only a 2 degree difference in the cutting angle between the breaks and mains so they cut in fast. Using a finer grit lap slows the rate of removal down so I don't overcut the facet.
A shot of the mains all cut in and ready for polishing
A finished pavillion! I did the final pre-polish and polish on my Darkwing lap charged with 5,000 grit diamond and aluminum oxide using the same steps as on the break facets. Time to transfer and swap ends now.
Here the stone is set in the tranfer jig, ready to be bonded to the cone shaped dop stick underneath. The  pegs in the dop stick are both rotated to the same position so that the facets on the crown and pavillion will be in alignment when the transfer is finished.
The stone is now pressed into the cone dop, that has had the same super glue applied to it as I used to initially bond the stone when I cut the pavillion.
After setting in the transfer jig overnight, I've removed the dopsticks that are now securely bonded to each side of the stone. Here I've wrapped the cone dop side in a wet paper towel before I apply heat to the flat dop side.
Applying heat to the exposed dop stick about 1/2 to 3/8 inches in back of the stone.  The heat conducts up the stick and will loosen the bond on that side so that a light tap will remove the dop stick while leaving the cone dop, under the wet  paper towel, still securely bonded. 

A side note: some gemstoes are sensetive to heat and will require different transfering techniques than what I'm using here. I use several different ways of transfering stones but it would recuire a small novel to list and illustrate them all. 
The transfer is complete. Now I'll leave the stone for several hours just to make sure the bond is tight and any heat that might have gone through the stone is gone.
Ok, time for the final push! This has turned out to be a bigger project than I expected and now I've got a lot more respect for the people who write those big long novels. Anyway, I'm not going to bore you with a rehash of each step. I'm using the same laps and the same steps for cutting , prepolish and polishing this stone. This is a shot of the crown break facets, the first step in cutting the crown. This is in the prepolish stage and they've been cut at the same indexes I used on the pavillion breaks. The angle I used on these is 40 degrees.
Same cuts but now polished.
Here's the start of the crown main facets. By changing the angle to 36 degrees and the index to the same as on the pavillion, I get this little wedge that I'll walk right down, almost until it meets the girdle. 
Here's the finished main facets. Like I said above, I walked the facets down the stone until they almost touched the girdel, then brought used the prepolish and polishing step to make the final meet with the girdle facets
This is a shot of the final stage of cutting the crown, doing the table. I've cut the star facets using an angle of 25 degrees and indexing at 6, 18, 30, 42, 54, 66, 78, and 90. this gives the main facets their kite shape. A good example of the star facet is in the next picture. The table is cut down until it meets with the junction of the top of the main facet then polished using the same laps and steps as every other facet.
Aaaaand, presto! a finished stone! You can see the triangular facet at the top of the stone. That is the star facet. Also you can see how they meet to give the main facets their kite shape. A little side note here. The table on this stones is what's called an elevated  table. This is something I like to do on a lot of the lighter stones. While it darkens the finished stone by a touch, it also hypes the dispersion, or fire. Dispersion can be exp;ained as the prism effect where the light coming out of a gemstone is broken up into its component colors. I'll freely admit to being a big fan of dispersion Lol. I get the elevated table by using that 25 degree angle on the star facets instead of going to a more standard angle of around 18 degrees.
Another shot of the same stone, This time you can see the bubble inclusions at approx, 12 o'clock. These are hidden under some facets and are easily apparant to the naked eye. Flawless rough is very rare in most stones so it becomes the job of the cutter to get the most beauty a piece of rough can offer. Sometimes this means tucking an inclusion under a facet so it's effect on the stone is minimized.  Also it can be a mork of identification that this is a natural stone and not one that came out of a lab. There are many gemstones out there these days that are man made. Many take a trained gemologist to tell the difference between man made and natural gemstones so, don't necessarily look at these as flaws but rather a mark of authenticty.
I hope you've enjoyed my project as much as I have and come away from it with some knowledge about gemcutting. If you have any questions on faceting, machines, rough or cut gems, I'm only as far away as the "contact us" button on the top of the page. If it's a question I can't answer then I probably know who or where you can find it.