I don't know if it's the "best" way, but you should read Mythology by Edith Hamilton

It really depends on how deeply you want to delve into it, and how much you already know - if the sum of your expertise is Disney's Hercules and what little is taught in schools, I'd recommend Religion of the Ancient Greeks by Simon Price. It's far from complete, and may be a bit dated in places, but the subject is so great and so foreign to most, that a very basic grounding is needed before going into detail. Price was what I was given as introductory material in a 1st semester class on ancient Greece.
I am not myself enough of an expert to recommend much high-level litterature, but I was recommended Greek Religion by Walter Burkert on this sub, I think by a flaired user. Very thorough and interesting, but not for the uninitiated.

I always considered, for me, the most interesting approach to Greek mythology to be the works of Karl Kerényi.

Especially his later works on Dionysos and Prometheus.

Dionysos: Archetypal Image of Indestructible Life

Prometheus: Archetypal Image of Human Existence

Between around 1940 to 1970, he produced numerous works exploring Greek mythology, and in quite novel ways.

Also of great interest and worth is his correspondence with German writer, Thomas Mann, wherein the two great minds bounce ideas back and forth to one another involving myth and archetypes and purpose and what myth means.

Mythology and Humanism: The Correspondence of Thomas Mann and Karl Kerenyi