The approach is to define each of these terms. The exact way how this works depends on what you have in terms of observed data. For example P(A) could be observed data, or if not it could be a prior distribution. But for each of the links such as P(B|A), you would define an equation to describe what this relationship is. A simple one would be a linear regression type relationship.
My guess at what might be most useful here is to work through this Linear regresion example. That might help with facilitating the high level mental click to understanding