(Disclaimer : when I say 'Abstract Art' i really mean 'American Abstract Expressionism')

Abstract art is about retraining your eyes to stop looking for an image.

We are so used to scanning for objects in real life and in representational art.
You have to quiet that part of your mind. Abstract art isn't of anything. You're
not supposed to recognize objects or be dazzled at the artist's skill. Abstract art can be very simple; the artist is attempting to communicate feeling in a radically more direct way than representational art.

Take a look at Jackson Pollock :

Maybe you see a drunken jazz party. Stop that. This isn't a Rorschach test.

Now you think, "Man, this isn't hard. My kid could do this!" Knock it off, this isn't a skill contest.

Look. It's paint and surface, nothing else. Feel the swirls. Their energy. Their tangling. Pollock goes all the way to the edge of the canvas where it's just as busy as the center. Feel the tension as everywhere the eye looks, you miss something. It's hard to take in.

You don't have to like it. If you hate it, hate it passionately, for what it is.

Here's Rothko :

Not much seems to be here. Give it some time. How do the colors feel? Alone and in contrast? The borders - they're kind of smudgy. What feeling does that give?

Many people find Rothko's work terribly sad; maybe you feel the same way. If so, you're definitely beginning to get it. But you may feel differently altogether - as long as you're feeling something you're 'getting' abstract art.

Keep at it, keep trying. In my case, it came all at once staring at a Pollock. In an instant some circuit went off and I was all "Oh. My. God." From that instant forward I found myself saying "The only real art is abstract."

Try other "Abstract Expressionists" and other flavors of Abstract. It'll come.