Step1
Still Life With a Basket, by Paul Cézanne
Do you recognize something "real" in the artwork?
For instance, if you look at a still life, you may say, "I see an apple, a bottle and a chalice," and others likely will see those, too. Still lifes are usually (and maybe necessarily) examples of representational art in that they are representing an array of commonly recognized objects. They attempt to copy, even if in a subjective manner, something that's real.
If the artwork falls into this category of being recognizable as depicting something real in particular, chances are it's representational art. Other examples of representational art often include portraiture (persons), landscapes and wildlife.
Step2
Fresco in Palazzo Farnese (Rome)
Do you recognize something "fictional" in the artwork?
Do you "see something" in the artwork that others will likely recognize, too, but it's something that's "not really real"? A unicorn? A troll? A tree that grows humanoid hands instead of leaves?
If you do, this also counts as representational art. A depicted object need not lead an existence independent of human imagination.
Step3
Counter-Composition V, by Theo van Doesburg
Do you not see anything (obvious) depicted by the artwork?
If you're viewing a sculpture or painting, and it looks more like a "design" than like some immediately recognizable object, chances are it's nonrepresentational art. Sometimes this is loosely referred to as "modern art" or "abstract art," though the three terms are not by any means interchangeable.
Step4
Recognize the overall significance of the difference.
As we have seen, representational art claims some affinity for the objective, the universal or quasi-universal, the "real" (even if this "real" is "real fiction" as with the unicorn). This means that it's at the very least offering an interpretation of the world and shared objects therein.
Nonrepresentational art, on the other hand, is not referring to anything "outside of itself."
The significance here overall is that representational art, inasmuch as it points to something outside of itself, may be considered a commentary on something external, and this places it squarely in the realm of the social (and even political), whether that's obvious at first blush or not. The cultural productions of a society reflect how that society views itself and the world around it.
Nonrepresentational art, on the other hand, may only offer commentary on art itself. One might call it "art about art." The onus is almost entirely upon the viewer to provide and/or comprehend any meaning. Please see Resources at the bottom of this page.
Nonrepresentational art commenting on art eventually leads back to the social, but only indirectly as compared with representational art. You may find that nonrepresentational art concerns itself with the HOW of artistic/cultural production rather than with the WHAT of artistic commentary, and yet eventually this distinction (often called "form versus content") blurs. It is often said of modern art and literature that form IS content, or at least that there is no absolute distinction between the two.
Representational art uses form to denote a ready-made content, whereas nonrepresentational art amplifies form for its own sake.