Though classical music appeals to many people, the diversity, complexity and even the mystique of "Classical Music" can be rather intimidating. Granted, there is much to know, and much to learn, concerning this music (many people have devoted their lives to studying obscure facets of musicology), but the encouraging thing about this art form is that you can enjoy what you are hearing without knowing exactly why.
So, while detailed study, investigation, reading, whatever, may perhaps enhance the enjoyment of the music even further, a scholarly approach is fundamentally not required. All that is necessary is a desire to explore and discover new musical territory. The classical music genre is rich enough to provide a lifetime of wonder and surprises, and a nearly limitless potential for discovery makes the journey well worth the effort.
OK, now, "Where do I begin?"
Some ideas on methodologies for exploring and learning about music.
A few thoughts on historically-informed performance practice.