Trained ears.

In your case it should be pretty simple - use well recorded piano music that you know well and ask yourself which system or change gets closer to the sound of a real piano in a real room

in my case And given the types of music I am most experienced with I use a variety of rather sparsely recorded folk music and look for system changes that get closer to the experience of real musicians in real space. 

Listening for gross frequency response issues or the top and bottom of the range is besides the point if the system is messing up the small details

This is a nice tool to play with.

http://harmanhowtolisten.blogspot.com/

Complicated. First of all I try to figure up what annoys me most in what I hear and then go from there. Drive flow and coherence are what should be done right before everything else, I believe. Assuming that speakers are more or less okay, this means that you start at the source. And the best source is tape.

Agree with the above posts, plus sitting in the sweet spot with eyes closed helps quite a lot. Also, if you wear glasses, remove them.

Tom

I agree with all above posts.  Listen to music that you are familiar with (or that you like and are going to listen to over and over).  Do the instruments sound real?  I’ll listen for drums...high hats / cymbals.  

Familiar music is key, critically listen, close your eyes.  

If everything is right, or close, you can go from critically listening / evaluating to just getting lost in the music.

If you’re trying to see what differences a wall outlet or power cord makes make sure to change only 1 thing at a time.  Power cords and outlets / power conditioners increase bass depth and weight, gives a darker background from which music seems to just appear and gives better highs in my experience.

It’s all system and synergy dependant but changing out pieces and then evaluating the difference is part of the fun.