Steel with some carbon content can be hardened (see Wikipedia) to make it, well, harder. The steel is heated until it's cherry-red and then quenched quickly in a bucket of water. The steel needs to cool very fast, so the piece being hardened is moved around in the bucket to avoid air bubbles from isolating the steel from the water and thus slowing down cooling.
Note that there are many variations of this process, and some (modern) steels can't be hardened like this. Please refer to more thorough sources for more information.
Tempering (see Wikipedia) is a process which reduces the excess hardness of (carbon) steel after it's been hardened. If tempering is omitted on a high-carbon steel, it will be as brittle as glass, and thus (usually) useless. Mild steel which has a small amount of carbon in it can be hardened without tempering it: this makes it somewhat harder.
First polish the piece of steel that's being tempered just enough to expose a shiny metal surface. Then heat the piece slowly, until it starts changing color. Once it's of desired color (i.e. softness) for your purposes, stop and let the piece cool slowly.
For more details, refer to the Wikipedia article on tempering.