“[the blind man] said that most men were in their lives like the carpenter whose work went so slowly for the dullness of his tools that he had not time to sharpen them.” Cormac McCarthy
There are many ways to sharpen edge tools. All of them are messy, time-consuming attempts at geometric perfection. Two planes meeting at an almost infinitely precise arris. How to make that happen?
Ultimately, the trick is to keep the back of the blade absolutely flat. Perfect blade geometry requires grinding back the bevel and lapping the back. Grind the bevel at 25 degrees on a bench grinder. For best results, use an aluminum oxide wheel, and dress it frequently with a diamond dresser. Lap the back with 220 silicon carbide paper on a piece of plate glass.
Use the same paper on plate glass to shape the bevel. The bench grinder will leave a hollow grind on the bevel. Let the bevel rest evenly, heel and toe, moving the blade side to side along the length of the paper. Observe what is wearing away, and adjust your position and movements accordingly. To avoid tearing the paper, draw the edge rather than pushing it, and try to develop a figure-8 pattern. As the hollow-grind disappears, the bevel becomes a flat plane and a distinct burr or wire edge can be felt on the back.
You can continue honing on successively finer grades of abrasive paper. A little water on the plate glass will stick the sheet and makes it easy to change grit. Finish up by stropping with diamond paste or auto body polish on a flat board. Clean, cheap, and good enough for most woodworkers. I believe this method tends to round the bevel and the back slightly, sacrificing the perfect geometry but achieving a quick, sharp edge.
Waterstones are small bricks of aluminum oxide that can be quickly lapped flat and just as quickly worn hollow. A good beginning set of stones, an 800 or 1000 grit stone, and a combination 1000/6000, will last for several years. They require attention. The 220 grit paper on plate glass works well to flatten waterstones, and the paper will work on the stone after it’s initial abrasion has been used up on the steel. So, an 85¢ sheet of paper should last through an entire sharpening session.
Build a box and a support for the stones. Keep the water clean and warm, and don’t splash it about. The combination of aluminum oxide and iron oxide stains wood, permanently. Spend as much time as necessary lapping the back, coloring the blade with a magic marker if you are unsure about what needs to be ground away. Move the bevel in that gentle figure-8, always drawing the edge to avoid gouging the waterstone. Lap the back, then the bevel, until a burr can be felt on the back, then move to the next finer stone. A sharp edge will shave. Be sure to wipe the blade dry and apply a coat of oil.
“…but they [craftsmen] keep stable the fabric of the world, and their prayer is the practice of their trade.” Siriach [Ecclesiasticus; the Apocrypha] 38:34