Most cutting tools require sharpening. There are various methods and tools for sharpening. For very sharp tools like shavers, they often call it honing rather than sharpening.
The most traditional method is to use whetstones. Whetstones have different grits or hardness/fineness levels and are used in progression from rough to smooth.
You can also use files, leather strops, abrasive compounds embedded in cloth, wood or leather, the palm of your hand, cardboard, the bottom of a plate or just about anything abrasive.
There are several major steps in sharpening anything.
- Fix the "geometry" if necessary. This is the shape of the edge or the blade. Sometimes, after sharpening over and over or through damage, the blade edge can end up with the wrong shape. Sometimes the heel stick out and doesn't allow the edge near it to touch the cutting board. Sometimes the edge becomes convex or curved, sometimes there is a major chip, etc. Fix the geometry on an appropriately rough stone first.
- Set the bevel. The bevel is the cutting edge. Many knives and razors have a bevel that is at a different angle than the surface of the blade just before the bevel. Wedges and many Japanese knives have the bevel angle and the side of the blade, the same angle. It's important for the bevel to be "set" so that a clean edge can be honed or sharpened as the bevel gets dragged along the abrasive.
- Grinding. Sharpen the edge with successively higher grits stones or the equivalent. Each grit level will remove material from the blade by scraping with tiny particles either on the surface of the stone or strop or from particles suspended in the water on the stone, called "slurry." The scratching will leave scratch marks. As the grit level increases, each stone should remove the scratch marks of the previous stone and replace them with finer / narrower scratch marks. Do not move to the next stone in the progression until you've removed the scratch marks from the previous stone.
- Polishing. At higher grit levels, you're not longer removing material from the blade, but mostly polishing and moving metal around. You're making the edge more flat and less jagged. Jagged edges can cut like a tiny saw, but straight edges are important for the quality of a shave on a shaver and apparently last longer than jagged edges.
- Stropping. The very top of the edge can bend or have bits of material and unevenness on it. Stropping pulls a blade across leather or other final fine surface to straighten the tip of the edge and remove bits of extra material from the edge for the final edge.
If a knife or a razor has recently been sharpened or honed, stropping may be the only thing required. With a knife, you can do this on a honing rod and with a razor, a strop.
If the tool needs sharpening, the key is to figure out how "gritty" you need to get. If you need to "fix geometry" on a big knife, you may need to go all the way to a 150 grit diamond plate if you're grinding a thick section of the heel or somethig, but typically you don't need to go much below 1000 grit. If it's just a bevel set, I use a 1000 grit or a 3000 grit depending on how much works there is. I've seen some people boast that they bevel set their razors on a Botan Mikawa Nagura, but I think that's more to show off than for any practical reason.
After that, there is a progression depending on the mood I'm in, how much time I have and how sharp I want things to be.
For razors, if there is no bevel set needed, I'll usually just do a Mikawa Nagura progression on a Japanese natural stone finishing stone. The Mikawa Nagura are small stones that you rub on a base stone, usually a finishing stone, that creates a slurry from the smaller stone - the nagura. The slurry on the Nagura mixes with the slurry from the base stone to create an effective abrasiveness that is different from the base stone. A typical Mikawa Nagura progression takes you through successively finer nagura until you end up with the "Tomo Nagura" which is a nagura made from the same stone or similar stone as the base.