This is a really tough topic to just read about. You pretty much need to dive into the software to really understand how to do FEA.
Basically FEA is a breakdown of a physical object (solid or liquid) is to small "elements" or nodes and the software calculates all of the equations that you have learned in your undergraduate classes (Statics, Dynamics, Heat Transfer, etc.) for thousands of nodes and creates a visual representation of how that object is impacted by what you have applied to the object.
If you really want to learn FEA I would recommend taking a class. The reason there aren't many books on the subject is due to the fact that is pretty much just learning to communicate with the software and interpreting the results using your engineering principles.
Hope that helps!