Summarize the following:
Most uncut gems are oddly shaped so you may need to grind it down. Roughly grinding the outsides of the gem will make it closer to the size and shape you want. Hold the gem between your fingertips and carefully polish it on a 1200 grit lap.  If you have a lot of rough to remove, use a 260 grit lap. Since faceting machines are expensive and not usually available for rent, see if you can take a few faceting classes to become familiar with using them. If you want to buy one, find one directly from a manufacturer or look online. Heat a dime-sized amount of dop wax on the end of your dop stick. Hold it near a flame so the wax softens and becomes pliable. Stick the base of the gem that will be mounted into the wax. The faced surface of the gem should be exposed.  Let the wax cool before you grind it so the gem stays on the dop stick. Once you've gained experience, consider using superglue or cyanoacrylate adhesives instead of wax. These are less likely to break off or damage heat-sensitive gems such as opals. Use a 1200 lap disc on your faceting machine to cut the circumference (girdle) of the gem. Set the angle to 90 degrees so you can make symmetrical cuts. Don't lock the index wheel on the machine so you can move it freely and have more control over cutting.  The outline you cut will depend on which shape you've chosen. For example, you'll make a rectangular girdle for an emerald cut. Consult the machine's instruction manual for specific instructions about each style of cut. Wipe the gem clean with a microfiber cloth. This will remove the coarser grit that's transferred to the gem. Take the coarser lap disc off of the machine and put a pre-polishing lap on the machine. Find faceting diagrams for the shape you're cutting the gem. A diagram will tell you how many facets to make and at what angles to make them. Polish the facets against the lap until the surfaces of the gem are smooth. To get the cut you want, you may have to reheat the dop wax, remove the rough, and reposition it in the hot wax. Heating the stone along with the wax will not harm it. Put a polishing lap on your machine. Take the small spatula that came with your oxide polish and dip it into the polish so a peanut-sized amount is on the end of the spatula. Run the machine and spread the polish over the lap in a smooth even layer. This will buff your new gemstone until it sparkles and will help remove any grit or imperfections leftover by the faceting process. To remove the finished stone from the dop stick, warm the wax near an open flame so it softens. Then pull the stone away from the wax.

Summary:
Use a faceting machine to preform the gem. Secure the rough gem to a dop stick using warm wax. Grind the outlines of the stone to shape the girdle. Wipe grit from the gem and put a pre-polishing lap on the machine. Cut the facets according to the shape you want. Charge the polishing lap with an oxide polish. Polish the top of the cut gem against the polishing lap.