Mild steel, which does not harden with the usual methods, can be hardened to a degree with a special solution called Super Quench.
Steel is a wonderful material. It can be treated to be harder and more brittle, or tough and springy, or soft and malleable. In its simplest form, an alloy of iron and carbon, it can have a wide range of hardness, toughness, and malleability. Adding other elements (chromium, vanadium, manganese, silicon, molybdenum, etc.) changes the properties as well, giving corrosion resistance, variations in hardness, machineablility, and many other properties. The exact alloy composition governs the possibilities.
When steel is heated, the molecular structure changes. The iron atoms arrange themselves roughly at the corners of a cube, in a repeating lattice. When not specially treated, the carbon atoms sit between them at the center of the cubes, in a "body-centered cubic" lattice. When heated to the right range of temperature, the lattice expands and the carbon atoms move from the middle of the cube to the center of one of the faces, forming a "face-centered cubic" lattice. As the steel cools, the carbon atoms move back to the center of the cubes, but it takes some time for this to happen. If the steel is cooled quickly enough (quenched), the carbon becomes trapped in the faces of the cube. In this position, it makes it harder for the iron atoms to move past each other, and the steel becomes harder and more brittle. The more carbon (to a point, close to 1.5% by weight), the harder and more brittle the steel will be. Another treatment, tempering, can reduce the brittleness while keeping most of the hardness. Yet another treatment, annealing, can return the hardened steel to the softer body-centered cubic structure.
Mild steel describes steel that is primarily iron, with a small amount of carbon (roughly between 0.05% and 0.30% by weight), a little manganese, and negligible amounts of other elements. The usual quenching methods, plunging the hot steel into water or oil, do not trap enough of the carbon in the cube faces to appreciably harden the mild steel. The steel is almost as soft as before the quench. Blacksmiths working on mild steel will routinely cool their piece in water, confident that it won't become brittle.
To get the most hardness out of mild steel, the steel needs to be cooled as fast as possible. Water removes heat faster than oil, but the steam that forms around the hot steel acts as insulation at the same time it is carrying the heat away. Only as the steam bubbles collapse or move away does more water contact the steel, and then some more energy is taken forming more steam. Dissolving salts in the water makes the bubbles use more energy when formed; a brine quench will harden (and embrittle) more than pure water.
Old blacksmithing books call for several exotic quench fluids. Mercury was used by some; now we know the dangers of mercury vapor. The high heat capacity and high boiling temperature would indeed make mercury a fantastic quench, but it's so terrifyingly poisonous that there's no way I'd consider actually using it. Lye (NaOH solution) is another excellent quench that's dangerous enough I'm never going to use it.
It was a need for a very fast quench that drove Robb Gunter, working at Sandia Labs, to experiment with safe quench liquids. He knew that a brine solution would have higher heat capacity, and that the vapor jacket formed by hot steel in liquid quench was the most significant obstacle to a faster quench. Brine reduces the vapor pressure a little, so that helps, but also adding a surfactant drops the surface tension (making the vapor jacket break up more quickly), and a wetting agent improves that effect. He and his coworkers called it the "soap solution quench", but it is more often called "Gunter's Super Quench" or just "Super Quench". The recipe is approximately:
4 1/2 to 5 gal water
5 Lbs table salt
32 oz blue dishwashing liquid
8 oz Shaklee Basic "I" or 7 oz. unscented Jet Dry or Simple Green (wetting agent)
The Super Quench solution needs to be stirred up before use, and the usual movement of the hot piece while quenching has its usual beneficial effects. Any of the wetting agents will work well; use as much as is recommended for 5 gallons of water. The color of the dishwashing liquid is important only for monitoring the solution's usable life. When it turns greenish, then it's time to replace the quench. To keep it fresh longer, store it in a covered container.
Mild to medium carbon steel (from around 0.15% to 0.45% carbon) can be safely quenched in Super Quench. More carbon, and the steel is likely to shatter. The steel will probably be in the low to mid 40s on the Rockwell C scale, where a water quench on the same steel would be in the low 30s, and tool steels quenched in the correct way will range near 60.