in my opinion there is really no textbook way to explain this kind of thing. When i try to find out what key a song is in, I can 'feel' the root. My ear hears it and I just know it somehow. As for defining a key, when you say something is in the key of C, it means that the song is based roughly around C as a singular note or chord. It may not necessarily start or even end on C (though it usually does), but it will be the most played and emphasized note.

True you could use any mode of C (A minor, E phrygian, G mixolydian, etc.) and it would sound okay, but when I solo over a chord progression I don't lock my mind into thinking that I'm playing C ionian. Though I may use the C ionian shape on the fretboard, I focus on the chord tones of whatever chord is currently being played and try to make all the changes flow smoothly so the listener doesn't notice.

For beginners to theory, start with textbook definitions and simple exercises. I was at that point too, and as I became familiar and confident with it, I took the theory I learned and 'warped' it in a way that made it mine so I could work with it in an efficient way for me. Everbody has their own way of viewing how it all fits together, just like in perceiving all of life, and you have to find your way.