I have a number of specimen photos posted on the Fossil page here that are cut and polished by hand (one shown below). Primarily, the specimens shown are calcitic and are relatively soft. One specimen is silicified. My methods are labor intensive but fairly easy to do.
1) Unless you collect a specimen that is fairly flat to begin with, you will need to cut the specimen (or have someone else cut it for you).
2) I use an old Felker Di-Met diamond saw. This is a contractor’s saw with a 1 HP motor. The blade is a Black Diamond brand, 12″ diameter which will allow up to 155 mm maximum cut depth. I use water from a garden hose through flexible nozzles to lubricate during the cutting. I have the saw on a roll around table and I use it outside as water sprays everywhere under use. The saw has a sliding table but no vise. I installed a lip on the back side to help guide the material into the saw. See photos.
3) Tile cutting saws are available fairly inexpensively at big box stores. These saws are designed to cut marble and other stones as well as ceramic tile. The stones being cut are all fairly thin so the motors on these may be underpowered for cutting thick materials. My saw had a 1/3 HP motor on it when I first acquired it and I was able to make that work by slowing down the progress into the blade by not pushing as hard. This could also work on the smaller tile saws.
4) Diamond saw blades are expensive so a saw with a vise is best to stabilize the specimen. This will also give a smoother cut. As I said, mine has no vise so I go to great effort to make sure I can hold the piece steady throughout the cut. If you wiggle the piece you can bend and ruin the blade.
5) All of my polishing is done by hand. I do not own any type of lap at this time. I use automotive wet/dry finishing paper for all but the final stage. All papers that I use are wet and then placed on a 1/2 inch thick piece of Lexan that I have propped on an angle in a utility sink (I’ve also done this outside while sitting on a lawn chair with the Lexan in my lap). I use these grits of paper: 100, 220, 320, 400, 600, 800, 1000, 1200 and sometimes 1500 and 2000.
6) I start with 100 grit paper to get out the saw marks and make the piece flat. This is the most time consuming part of the process. It is a matter of scrubbing the surface against the paper. The paper is kept wet as needed. Any time the piece is lifted off the paper to inspect progress, the paper must be rinsed off before placing the piece back on the paper. This step removes any tiny chips that could be trapped under your specimen when you start sanding again – this would put a big scratch in your work and cause you to start all over. Always rub the specimen in one direction only so the scratches you are putting on the specimen from the sandpaper can be distinguished from the scratches already on the specimen. Examine the surface with a 10-x hand lens to be sure all sanding marks are going in the same direction over the entire surface of the piece. Once this is accomplished, switch to the next finer grit paper and turn the specimen 90 degrees before starting to sand so the new scratches can be distinguished from the previous. Continue this process all the way through to the finest paper you are using. Be very careful to keep the specimen flat during this process so it doesn’t rock and make the surface rounded or beveled.
7) For a final polish, I use Cerium Oxide abrasive powder on a wet 1/4 inch thick white felt pad. The pad is placed on a 1/2 inch thick Lexan piece for support. This is a rubbing process just like the sanding although your motion can now be circular or linear. Always inspect the pad for tiny rock chips that may flake off your specimen as they will absolutely ruin all of your work.
8) This process works very well for any specimen that is calcitic. On small specimens the sawing can even be skipped. Specimens that are Dolomite can be done too but it requires a bit more elbow grease as they will be harder. Silicified specimens are tough as they are considerably harder and not really practical to do by this method.
9) A four inch diameter specimen will take about 2 hours from start to finish using this method and it’s a great workout for you arms!.
10) The silicon carbide wet/dry paper can be obtained at automotive finishing suppliers except for the 100 grit. I get that and the Cerium Oxide from Kingsley North (they deal in lapidary equipment and supplies).
11) Note that not all specimens will exhibit a mirror finish. That depends on the grain structure of the specimen. Some are fine grained and solid while others are coarse grained and porous. Either way, the internal structures of some fossil can be beautiful and help with identification.