hydrogen peroxide treatments work best with the steel at a pretty high heat not forge heat mind you but still a black heat, where you can see the water vapor on the steel driven off, we use a propane weed burner.
the easiest cheapest route is stove polish but it may not be at all what you have in mind
it sort of depends on what you mean by blackening and what you mean by steel. A chemical cold blue like what Birchwoodcasey offers is very different than both the above. We buy various Birchwoodcasey bluing solutions and make our own as well (nitric acid, cupric sulfate, selenious acid)
When it comes to "true" bluing (which is often black or dark charcoal) its often a heat treatment with carbon or chemicals, as applied in gunsmithing the processes have changed over time with the carbon content of the steel employed in making the parts, it gets really interesting when you look at some guns that may have up to three different bluing processes employed.
some basics
Bluing (steel - Wikipedia))
Passivation Nitridization Carburization Case Hardening Restoration Articles - All About Bluing (ARTBLUE.HTML) (good basics of the various processes employed at one point or another)
the bluing most suitable to mild steel, is slow rust bluing, which is highly labor intensive in that you card off all the red iron oxide which is a larger molecule and leave only the black iron oxide which is smaller with a tighter molecular bond, then repeat the process till you get an acceptable finish (which is covered as "RUST BLUING" by Bill Adair in the article above)
there is a great amount of confusion in bluing terminology, with many names describing the same or nearly the same processes, in British parlance substitute "blackening" for "bluing" the actual finish you get depends on the process and the steel that is employed, from a deep black to a temper blue