A woman asked me today "How do you look at modern art?"  She has been collecting realistic art, but finds  herself intrigued by abstract art, and in her words, "art that doesn't look like something".
My advice - don't over think it. We are all drawn instinctively to particular imagery, be it through the color, size, or energy of the piece.  Shank and Cole are two artists that come to mind; Shank paints in a very emotional, intuitive style with bold colors, lines and squiggles and circles.  Cole, on the other hand, does use bold color but her pieces are more studied, thought out - she has more control of her piece.  And it is funny to see the reactions in the gallery, because much like real life, the women tend to gravitate towards Shank's work, and men seem more interested in Cole's abstracts.  I like them both and would be hard pressed to single out a favorite.

Speaking of what 'touches' us with art - that is what I like about being able to choose the art in the gallery.  I find equal beauty and appreciation in a petite painting of a hummingbird AND the vastness and strength of a 40x60 inch encaustic work; two completely different pieces of art, and side by side I could  not choose which one meant more to me.

When I evacauated New Orleans, I had to choose, quickly, what to take with me. My daughter, my pets - those were obvious choices. But the art that I was able to actually fit in the van was another story, and ultimately I dashed with a 4x4 inch line drawing of a sparrow, and an 60x60 inch painting of a goldfish.
And my husband.  Which in hindsight was the wrong choice!

But back to looking at art, and 'how' to view art - trust yourself.  Trust your instinct, trust your taste, and just go for it.  It does not have to fit in with the rest of your house, and it sure as hell does not have to match anything.  All you have to do is love it.