Song breakdown

It seems the most effective way of teaching yourself is to learn the concept behind your favorite songs instead of just studying theory with no context, but when you break a song down how much time do you put into learning a hard solo for example and what does it mean to effectively learn the theory behind the song?

The most effective way of learning theory is to apply it in some way. Reverse engineering the theory from songs is absolutely an effective way to do it.  But you need some overall context in order to do it that way.  You have to start with some basic understanding of the concepts you are attempting to use in order to know how to apply it.  For example, when you are learning a solo, then trying to understand what scale the solo is using.  You have to have some understanding of notes, scales, intervals in order to know which scale one is correct. 

And conversely, knowing some basic scales and being able to play them can help you better figure out the solo in the first place. 

This is why I stress the importance of keeping theory & practice learning at the same level or pace.  Make sure you are learning theory concepts that are directly related to the technique or physical skills you are learning and working on.

To identify the theory concepts that explain what is happening in a song means you can name the notes, chords, key signature.  On a deeper level it means you understand the scale degrees that the melody or solo instruments are are using and how they relate to each other, how they relate to the chords of the song and what the other instruments are doing.

Hope that helps.