Here is an excellent, reasonably practical introduction to using and understanding a spectrum analyser. If you don't know much about Fourier, FFTs, windows, and calibrating then this is a good start.
http://literature.cdn.keysight.com/litweb/pdf/5952-8898E.pdf h/t to SomptingGuy for tracking this down yet again.
If that is a bit too dry then ElectricPete recommends www.dspguide.com
This looks to me like signal processing with attitude, entertaining and a good intro. It might well tell you everything you need to know, and the approach is about as non-mathematical as is practical.
This has more details about FFTs
http://www.science.unitn.it/~bassi/Signal/NInotes/an041.pdf
Here is an excellent discussion of the philosophical details of FFTs and wavelets.
http://engineering.rowan.edu/~polikar/WAVELETS/WTtutorial.html
This is Tom Irvine's website. He has written many useful papers on real signal analysis problems. There are also a large number of tutorials and examples there. http://www.vibrationdata.com/
Art Ludwig is a physicist (I think) and contributes to the alt.sci.physics.acoustics newsgroup, and is very interested in setting his stereo up. His website includes a lot of room acoustics theory, and psycho-acoustics.
http://www.silcom.com/~aludwig/
Lecture notes on a course in hearing. Seems to be biased towards music and psycho-acoustics
http://www.biols.susx.ac.uk/home/Chris_Darwin/Perception/Lecture_Notes/Hearing_Index.html
Bruel and Kjaer publish many useful primers and handbooks https://www.bksv.com/en/knowledge/library/primers-and-handbooks#
