Quick answer before this good question gets closed due to technicalities.
"Jazzing up" a song means realizing the same or similar or at least compatible-with-the-melody harmonic functions with more ambiguous, detailed, complex or just different and surprising chords. In order to be able to do that, you first have to be familiar with basic elemental harmonic functions. And to learn that, you (1) learn to play and accompany melodic (some might say, old-fashioned) pop songs by ear, as melody and chords, and then you learn (2) ways to support the same melodies with more or less different harmony i.e. chords.
For example: a simple I - IV chord turn. In C major, you have a chord progression C - F. Example steps to jazz this up more and more:
1 : C - F
2 : C7 - F
3 : C - Cmaj7 - C11 - F
4 : Cmaj7 - Gm7 - C11 - F
5 : Cmaj9 - Gm9 - Db9 - C9 - A/C - Gb13 - F13
Instead of simply turning left, you do somersaults, moonwalk and flirt with the ladies in the front row. But essentially it's still just a turn left. If you don't understand the basic stuff, you can't jazz it up in a sensible way.