The hamon (pronounced "huh-mown") is a Japanese invention, in popular culture most widely recognized on the traditional Katana. The development of the hamon, along with the Katana itself is attributed in legend to the swordsmith Amakuni Yasutsuna, around 700 AD.
The hamon is a visual effect, showing up when etched as a wavy line across the surface of the steel. The hamon is caused by differential hardening; one part of the blade, the cutting edge, is hardened (via quenching in water or oil from critical temperature), while the other, the spine, is kept soft and tough, and so less prone to breakage. When etched, the acid eats away more at the soft section, and so shows up darker, and less at the hard section, showing up lighter, sometimes with a dark band where the two meet.
Remember, a blade is most effective when it is tough (and so, soft) enough to take a lot of stress without breaking, yet hard (and so, brittle) enough to hold an edge without deforming. Differential heat treating increases the hardness of the edge, yet keeps the spine tough. This means it's both tough enough to take a beating, and hard enough to perform without losing sharpness.
So, differential hardening produces both a physical (hardness-toughness) and an aesthetical (hamon) result. Pretty good yield with no drawbacks. Now then, on to actually making it.
Note: I've only made a few blades with hamons, and am by no means an expert on the subject. This is my research, personal findings, and advice I've picked up along the way.
As you know, steel converts to a very hard, brittle state, when it is heated to critical temperature, then the temperature is dropped to nearly room temperature at a very rapid rate, using a liquid like water or oil.
So to keep the spine of the blade from hardening, it just needs to be cooled at a slower rate than the edge.
The way to do this is an insulating clay; something that keeps more heat in the spine, for just long enough to not convert to a hardened state (known as martensite). This way the blade is quenched, the edge hardens, the spine retains enough heat for enough time to keep from converting from martensite, and you have a deferentially hardened blade.
That's the science for you. On to the practical application.
First of all there are the materials. Not all hardening steels will produce a visible hamon. Basic carbon steels, such as 1095, 1084, 1075 will do it, with W2 producing some absolutely gorgeous hamons. 5160, (of which springs are generally made of) will usually not yield a hamon. You'll have the physical properties, but not aesthetic ones. Files and rasps tend to be close in composition to 1095, but I've found it's hit-and-miss in results with them.
As for the insulating clay, there are two basic clays that most smiths use (these are aside from traditional Japanese clays, usually a certain mix of clays and ash), Satanite, a clay used for the most part to coat forge insulation, and Rutland's Furnace Cement, a clay used to seal fireplace bricks. Some smiths use a mix of the two. I found the furnace cement at the local hardware store for three bucks, worth at least a dozen blades, so that's what I use (can't beat cheap+effective).
For the quenching medium, whatever you normally use for quenching. Water works (it's also the traditional method), but I figure about a %50 fracture rate on my blades; water often cools too quickly and the thermal shock cracks the blades. I've since switched to largely an interrupted quench: quench in hot brine for three-four seconds, then finish off in warm canola oil. Different mediums will produce different yields.
Finally there's the acid you need to etch the steel. The standard medium that produces the best results is Ferric Chloride, often to be found at radio shack. Lemon juice is said to work, though I haven't gotten any results from this. My usual is boiled vinegar; make sure the blade is clean, immerse it in the vinegar, pull it out every few minutes to rub off the oxides.
Applying the Clay
Tanto with applied clay, done in the traditional Japanese method, by Dave J Friesen
The thickness varies. I've personally gone for approximately the thickness of the spine where it covers, so if the spine is 1/4", the layer of clay is 1/4" as well. Too thick, and what happens is during the quench the edge hardens, but enough residual heat is left over in the spine that it spreads into the edge, overtempering and softening it. If the layer is too thin, the spine as well as the edge hardens. It's worth experimenting to see what yields the best results.
Try to keep at least a centimeter of steel exposed between the clay and the cutting edge. This keeps residual heat from ruining the temper.
As for the shape you apply it in, it's entirely up to you. The hamon shows up as a ghosty gray line, so flames or whisps are pretty cool. However, until you get it down it's tough to get details (again, too thin of clay will allow the steel to harden). You can go with the traditional Japanese waves, just slather it on, or create images. You can get some very interesting results.
So really, have fun with it. It's kind of tough to apply the clay exactly where and how you like, and until you get some practice the hamon is rarely exactly how you originally plan it, but you can still do some pretty cool stuff.
Quenching and Tempering
There isn't much to say here that hasn't already been covered. Standard quenching. Heat to critical; where a magnet no longer sticks, plunge in oil or water (quench), stir back and forth in a cutting motion. Stirring side to side can warp the blade, and let me tell you that is no fun to try fixing. The clay tends to soak and fall off as the blade finishes cooling, which is ok.
Temper as one usually would; 350-450 F, depending on the steel, for at least two hours. Again, time depends on the steel. There can be a misconception that having done differential heat treating, you don't need to temper. This can be true in the cases of certain steels, but especially for thinner blades and knives that are likely to come in contact with very hard materials, the edge is still very brittle and can chip.
Bringing out the Hamon
Hand sanding is just about the most boring, long, and tedious processes in knifemaking. Unfortunately, it's also vital for this step. I've brought out hamons only going to 1500 grit, but the higher the better. A satin finish (grit lines from the sandpaper still showing) makes the blade look flowing, soft, and smooth. This isn't ideal for a hamon, as the grit lines can still show up, looking dirty and ugly, and building up with oxides, rather than flowing and smooth. The ideal is to polish, meaning the blade surface is completely flat, down to a microscopic level. This gives the utmost appearance and attention to the hamon. This also means you've got a lot of sanding to do.
This is a full article on hand sanding, going down into the science of it and how to get a perfect surface.
Once polished, or as high a grit as you can get, it's time to etch. This is where the hamon becomes visible. While sanding you may have noticed a very faint light anomaly along the surface, where the hamon is, but etching is where it really shows up.
I've already mentioned the acids; ferric chloride if you want spend cash and get a really nice result, lemon juice or boiling vinegar if you're just experimenting and fooling around. Make sure the blade is very clean (grease or oil will block the acid), and submerge in the acid. Every few minutes take it out and clean off the built-up oxides, then replace, until the hamon is about as clear as you can get it.
Once you're satisfied, clean, wash, and complete the knife.
For your first hamon, and especially with unknown or substandard materials, it's likely not to be very prominent, or sometimes not even show up at all. There are a variety of factors as you know, including steel types, steel blade thickness, clays, clay thicknesses, quench material, finish, and the acid. Once you get it down however, it's a really stunning effect, both functional and artistic.
-Caleb Harris, the "Broke Bladesmith"
Knife and sheath featuring a beautiful hamon, by JS Ben Breda