In my opinion the single most important aspect of knifemaking is Heat Treating.

There are many methods used in the Heat-Treating Process. I will touch on the one's commonly used in my shop.
Heat-Treating consists of hardening and tempering in the simplest of terms. There are those using molten saltpots, cryogenic tanks and various eclectic methods. I use what has worked consistently for me over the years. 

After I forge a carbon steel blade to shape, the blade is brought to critical (non-magnetic) in the forge, and allowed to air cool. I do this process twice (normalizing). The blade is again brought up to critical and allowed to cool slowly in Vermiculite. Once the blade is fully annealed (softened) it can be ground, filed, etc. The purpose of normalizing is to remove some of the stresses imparted to the steel during the forging process (ie: heat, forging, etc;). The purpose of annealing is to soften the blade. After annealing the blade is ground from 50 grit to 220 grit. I usually leave the cutting edge a bit heavy so that I can remove any scale formed during the heat-treating process. I put a rosebud tip on my oxyacetalyne torch and heat just the cutting edge of the blade to critical, then quench the whole blade in oil. I will usually repeat this process two or three times depending on the steel used. I then need to temper (soften) the piece. This takes the brittleness from the blade along with imparting toughness. My tempering methods are quite simple.

I clean up the blade with 220 belts and then place the hardened knife (right after hardening) in a toaster oven until the blade is a straw or light gold color. Typically at 350-375 for 1 to 2 hours. This process is repeated three times with air cooling between cycles. I then put a small tip on my torch and draw soften the knives tang by bluing. The tang of the knife is brought to an even deeper blue to make it dead soft. Using the torch in this method allows a controlled differential temper (hard edge, soft spine, softer tang).

I have clay tempered before but usually do not use this method. There are times that I will heat the whole blade in my forge and only quench the cutting edge in oil. I will use this method on blades too large to effectively heat with a torch. I still temper these blades the same way.

For pattern welded damascus blades I use a different method of Heat Treat. Most of my damascus blades are forged from high and low carbon steels. The way that these blades are heat-treated is to fully heat the blade and quench the whole thing in oil. After cleaning up the blade I temper it in the oven. If it is a bowie knife I often will draw the spine to blue. 

Both carbon and damascus blades are cleaned up after tempering, ground, sharpened, tested and then hand sanded and finished.