The Dilemma: You don't want to look like an idiot on Antiques Roadshow.
People You Can Impress: architecture buffs, art collectors, absinthe addicts, and flappers
The Quick Trick: It all comes down to "flowery" vs. "streamlined." Art Nouveau is the decorative one. Art Deco is sleeker.
Both the Art Nouveau and Art Deco movements emerged as reactions to major world events; the Industrial Revolution and World War I, respectively. While both embraced modernist elements, they're easy to distinguish if you know what to look for.
Art Nouveau (it means "new art," but you probably figured that out) reigned from roughly 1880 until just before World War I. Art Nouveau embraced Europe's new industrial aesthetic rather than challenging it. It features naturalistic but stylized forms, often combined with more geometric shapes, particularly arcs, parabolas, and semicircles (think of the paintings of Gustav Klimt, or the arches of the Eiffel Tower). The movement brought in natural forms that had often been overlooked, like insects, weeds, even mythical faeries, as evidenced by Lalique jewelry or Tiffany lamps. The black and gold robe Kate Winslet doffs in the erotic portrait session scene in Titanic is quintessentially Art Nouveau.
Art Deco, on the other hand, emerged after World War I. In fact, the deprivations of the Great War years gave way to a whole new opulence and extravagance that defined the Jazz Age and the Art Deco aesthetic. The movement, prevalent from the 1920s until roughly the start of World War II, took it's name from the 1925 Exposition Internationale des Arts DÃ©coratifs et Industriels Modernes (say that ten times, fast), held in France and is characterized by streamlined and geometric shapes. It also utilized modern materials like chrome, stainless steel, and inlaied wood. If Art Deco dabbled with natural materials, they tended to be graphic or textural, like zebra skin or jagged fern leaves. As a result, Deco featured bold shapes like sunbursts and zigzags and broad curves. In fact, if you check out the spire of the Chrysler Building, the hotels of Miami's South Beach, or the "coffin nose" of a 1935 Cord Model 810, you'll be staring at the very definition of Deco.
Of course, you don't have to go outdoors if you're looking for Deco. Furniture from the period—like the black leather and chrome chaise longue by Le Corbusier or the Barcelona chair by Bauhaus giant Ludwig Mies van der Rohe—is still coveted by design aficionados and can be found in finer hotel lobbies everywhere.