Such beautiful styles of art - and so different too! I've tried to incorporate just a few influences from each movement in my glass paintings.
The Arts and Crafts Movement just sneaked in first, emerging in Britain in the 1860s. Art Nouveau followed close behind in 1880 - but in France & Germany. Art Deco, on the other hand, emerged as a reaction to World War I, and developed into a major style in western Europe and the United States during the 1930s.
The Arts and Crafts Movement was concerned with decorative arts - the design & manufacture of objects that are both beautiful AND functional. So a lot of interior design: basketry, enamelwork, floral decoration, furniture, glassware & stained glass,metalwork, mosaic, pottery, rugs and carpets,tapestry, William Morris & John Ruskin
Art Nouveau is also decorative: naturalistic but stylized forms, often combined with more geometric shapes. Think of the paintings of Gustav Klimt & or the arches of the Eiffel Tower, Lalique jewelry & Tiffany lamps. The black and gold robe worn by Kate Winslet in Titanic's portrait scene is quintessentially Art Nouveau.
Art Deco is much sleeker. It uses streamlined and geometric shapes in modern materials like chrome, stainless steel, and inlaid wood. The only natural materials used were graphic or textural ones, like zebra skin or jagged fern leaves. Look for bold shapes: sunbursts and zigzags and broad curves. Things like the spire of the Chrysler Building, the hotels of Miami's South Beach, the black leather and chrome chaise lounge by Le Corbusier or the Barcelona chair by Bauhaus giant Ludwig Mies van der Rohe.