Arkansas Medium, the hard, maybe a fine ceramic flat stone then a strop. All by hand. I figure while I might not get it as sharp as maybe I could on a machine, I do enjoy sharpening by hand and watching the hairs pop off my arm or leg when I get done.
Jigs allow anyone to be able to sharpen a knife. They also allow you to be able to hold perfect edge bevels which is great for aesthetic purposes. But after having used a Lansky system for years and having later learned to freehand sharpen, I can't tell any difference in "sharpness" in the real world.
Think about a single bevel edge. Its going to be 90 degrees on one side and say 15 on the other, essentially a right triangle. As long as the planes meet, it can be made as sharp as anything else, but the bevels certainly do not match. A sharp edge is made by bringing two planes together at a microscopic apex and then getting rid of any burrs created as best as you can. The planes do not have to match with geometrical precision. Making the planes meet and getting rid of the burrs is much more important to actual performance.
