really interesting thread...
so, I'm an art curator, in theory it should be 'easy' for me. But it really isn't.
I would partly agree with medea that it really helps to practice that visual eye. Some people are naturally visual, some find reading or listening a much easier way in. I definitely can't agree that visiting a museum if you're not visual is like looking at a newspaper without being able to read, though... that's the point of good interpretation, it gives you a way in. If you feel that lost, the museum, not the art, is at fault.
Stories behind paintings, be it historical, political, narrative or good gossip about the artist can all give you an insight into a piece of art. But no one sees it like the artist does, even something as simple as colours appear differently to all eyes, you will always view art through the mist of your own personal experience and prejudices. That can make it more interesting to you, or less.
Sometimes it's something as simple as the frame decoration that gets you involved with an artwork, sometimes the way the light hits the wall behind. All these are perfectly good ways of interacting with art.
Yes, sometimes the artist has a point they want to put across. Sometimes they don't. Sometimes you can like the patterns they make but not the point. Or visa versa. Just because it's art, doesn't make it right.
There are craftsmenship skills that you can learn to appreciate - the difficulty of a wood cut tool for example, or a drawing that is clearly very well proportioned. Composition is mostly about good balance, colours and shapes that help your eye to engage rather than pass over the image. If it's good you probably won't notice the effect unless you teach yourself to look for it. But then you force yourself to stand back from the engagement, so you rather miss the experience.
Art from 100 years or more ago is much harder to truly understand, because it generally reflects a different way of looking. When you lived in a world where you could look at a sheep and say - that's a 5lb joint of mutton; or where you had never seen the way a photograph ir the TV cut scenes off at the edges, your visual skills were different. We can't ever hope to properly see paintings like that as they would have been seen. The best we can do is try and spot signposts, but again, does the act of looking FOR something consciously, detract from the pleasure of simply looking?