A question I often get asked by my students is how to reharmonize a tune. This is a brief video outlining some methods I use. It is assumed that you are already familiar with jazz chord voicings, extensions/alterations & substitutions. Here is the leadsheet containing the reharmonization to Ode To Joy.

Reharmonization is a vast and beautiful area in which I continually encounter new insights and surprises. There are many books available on this subject, and transcribing reharmonized tunes by jazz greats will not only improve your ear, but give you a first hand look at how they approach improvisation on the new chord changes as well.
P.S. A minor slip of the tongue at 3:42 – the chord is a Gm9sus (not G9sus) and at 4:55 C#dim not C dim.