Two things make a person who they are. Those two things are a person's genetics and environment. Genetics is self explanatory. In this case, it is a physiological predisposition to crime. The environment part of a criminal's psyche is far more complex. In psychology, this is referred to as psychosocial and environmental problems. That's a fancy way of saying bad things that happen to them. These problems can be past or present. Every person has them, ergo every killer has them. The equation I use for creating a killer character is as follows:
History+Personality=behavior
Now lets examine the steps towards filling out every aspect of that equation.