It must begin with the evidence. From that evidence attributes, characteristics will be inferred such as occupation, living arrangements etc
But the profile is in essence statistics. It's a fascinating process though.
This is a great overview:
The process has gone through a variety of evolutions to try and increase the accuracy of the profiles.
"There are two approaches to offender profiling: the top-down approach, and the bottom-up approach. The top-down approach is the approach used by the FBI, thus called the American approach. It is called the top-down approach because it tries to fit crime details into predetermined categories or typologies."
"The bottom-up is the British approach. It aims to generate an offender’s profile by looking at the evidence. There are no ‘typologies’, the profile is data-driven and emerges as more and more details of the offence are known. It makes use of ‘smallest space analysis’, a computer programme that identifies correlations across patterns of behaviour. There are two methods to the bottom-up approach, investigative psychology, and geographical profiling."