I think I first started sharpening knives "for real" around the time I went off to graduate school and taught myself to cook. That would have been 1971. I'd been sharpening in some desultory fashion for some time, but had never really understood "what was going on in there", and was never able to produce a decent edge except by accident. I could, though, produce a fairly good point on a pencil, given a reasonably sharp pocket knife.
Then a housemate who is a fine amateur telescope maker and is generally extremely handy (Andrew Tomer, for those who know him) showed me some fairly solid basics. I began to get better at sharpening.
Eventually, having (or so I thought) gotten pretty good at this, I wound up one day at Tashiro's Tools in Seattle, where the proprietor was doing a cute little demo & lecture about knives and sharpening. He used a sheet of paper to point out some fundamentals. This does not by any means come across as well in print as it does viva voce, as it were, but we will do our best. Please bear with me, okay?
When you cut something, you must both sever and separate. You have to chop the fibers (or whatever) that make up the material, and then you have to separate the edges of the cut so that the knife itself can occupy the space between them. Otherwise you can cut the surface, but you can't get down into the material. If you use a dull or blunt blade all you do is crush whatever you're trying to cut. (Find a sharp knife, and cut a raw asparagus stalk with it. Now turn it over and cut the raw asparagus stalk with the back of the blade. Slight difference, eh?)
If, on the other hand, your edge is too thin, it bends or crumbles or breaks when you try to use it. That is, there are limits to the strengths of ordinary materials. Things that are hard enough to work when very thin are usually too brittle. Materials that are not too brittle are not hard enough.
One must find a usable middle position, with a material that is sufficiently hard, and an edge of suitable width.
Edge thickness is not the only issue; there is also blade-width angle. What I mean by "blade-width angle" is this: If you look at a cross-section of the blade, you see something at least vaguely like this: V The ideal blade-width angle is partly determined by the material you want to cut. (Rats! No, I didn't mean I'm cutting rats, I meant that I'd like to be able to pick some nice angle and sharpen all my knives to it; unfortunately, it is clear that such a course would be sadly suboptimal. Foo.) ...But back to the issue at hand:
The angle at the base of the vee is what I'm referring to. More accurately, half of that angle. (Let me expand that and draw a vertical line down the middle of it: \|/ -- the half-angle, the angle on either side of the vertical, is what I'm talking about. Don't you just love ASCII pictures? I sure do. Ahem.) Suitable half-angles seem to range from perhaps 15 or 20 degrees for veggies to maybe even as much as 45 degrees for some meats, though that is a bit extreme.
Tashiro-san did the niftiest little demo -- he took an 8.5x11 piece of ordinary bond paper, tore it in half, and folded one half in half. That fold became the object to be cut. Then he took the other half of the sheet and tried to use it as a knife to cut the fold, the way you'd ordinarily use a ruler. Turns out that a single thickness is not enough. It cuts a little and then it just bends over. Having demonstrated the "too thin" problem, he folded his "knife" in half, making a slightly thicker edge, and showed that it worked quite well. Then he folded it in half again two or three more times, producing this big blunt "knife", which tore the edge of the folded piece instead of cutting it. Most eloquent.
There are many ways to entice steel into the correct shape. Some people like the little oscillating machines that you just draw the knife through (I think "Chef's Choice" is a common brand); I tend to prefer Japanese water-stones, which are very (!) hands-on. Yes, it takes me twenty minutes just to get set up. Yes, it takes me half an hour to sharpen a single knife. Yes, I enjoy the process. I wouldn't do it that way if it weren't pointful. (Sorry, didn't notice that one until I had already typed it.)
Water-stones are a trip in and of themselves. My (admittedly weak) understanding is that there is a grotto somewhere in Japan where the base material is quarried; it is extremely hard stuff. They break it into pieces and grind it up, and then sift out various grit sizes. The grit is then mixed into some special clay and fired as a ceramic. The clay is fairly soft, and the ceramic that results (except for the finest grit size, for which they seem to use a different clay) is porous. The way you use the stones is to soak them in water for a while (basically until they stop bubbling), and then keep pouring water over them frequently while you are sharpening. As I say, the finest grit (6,000 particles per inch) is not as porous; those stones you just keep wet when you are using them.
There are many different grit sizes available. I use a coarse stone to begin with, but only if the knife I'm dealing with is rather dull. Once I've got something that vaguely resembles an edge, I shift to a 1200-grit stone. It is important to understand that 1200 particles per inch, which is fairly coarse as water-stones go, is finer than a "fine" grindstone you might buy in a hardware store. I think it's about like a "soft" Arkansas stone, but don't quote me -- I haven't researched this very carefully yet.
After I get a respectable edge at 1200, I go to a finer grit size and refine things a bit. Eventually, when I have an edge I really believe in, I take out the 6000-grit stone and polish the edge with it. You can't really remove a whole lot of material with a stone that fine in less than geologic time; that's not what it's for. It does, however, produce a mirror finish on the edge if you use it carefully.
My other favored implement is a "crock-stick" sharpener that has two sets of sticks and two sets of holes. The blue sticks are coarser, and go into the holes with the narrower angle. After you have an edge, you switch to the white sticks, in the holes with the wider angle. Of course, this doesn't let you choose your own angle, the way the water-stones do, but it's easy to use and it's relatively fast, and when you've already started cooking you don't usually have 30 to 50 minutes to kill.
I do not sharpen things professionally (try Howard Szafer), but I do sharpen people's kitchen or pocket knives for them sometimes. I also sharpen pen nibs.
Yeah, pen nibs. Remember, I do calligraphy. I happen to be left-handed, but I don't crab my hand around the way some of us do, and as a result I need nibs that have just the usual slant... in the other direction. (Sigh.)
Pen nibs being the small creatures they are, and water-stones being rather soft, I find I can't use them for this purpose. Fortunately, nature and The Gulch (Silicon Valley) have provided me with appropriate tooling. Gray, purple, and white ceramic IC packages are typically 96% aluminum oxide, extremely fine-grained stuff, about a thousand times as hard as steel. I use a Motorola 68000 processor as a grindstone. It is about the right size (1" x 3"), pleasantly flat except for the lid over the chip area (which you can avoid by using the underside of the thing, once you've ripped its tiny legs off [Aaaagghhhhh!]), and reasonably available. (Any sufficiently large ceramic IC of the right color will do, in fact.)
Remember, though, I'm left-handed. This means I'm pushing the pen across the paper much of the time. Merely grinding a nib to shape doesn't get me where I need to go. I have to polish them as well, or they're quite unusable.
For that I use brown ceramic ICs. They must be at least 6,000 grit per inch, if not considerably finer. They are also hard as the holes in hell. Big UV-EPROMs are the choice item here, because I've never seen a 64-pin (1" x 3") package in brown.
Over the years I've gotten fairly decent at making italic nibs. I even succeeded in building a few nibs for a right-handed friend, though it took a certain amount of fussing and tweaking.
When I talk about "hacking", this is the sort of thing I mean: dragging into the picture techniques and materials "from left field" (as it were), adapting what's around to whatever purpose is at hand. If you want to know how to go someplace from where you are, draw a map.