Decoupage (from the French word for cut) is the craft of decorating household objects, usually wooden furniture or papier-mache boxes, with pictures cut out of paper. It originated in the 18th century, to simulate the beautiful, intricately hand-painted lacquer items that were being imported at great expense from Asia, and early pieces are decorated with Asian art and themes.
It's simple to decoupage an object and achieve a fairly sophisticated look, and decoupage is therefore often thought of as a child's craft, but in its early years, it was a craze among the gentility. Just as all genteel young ladies were required to paint tasteful watercolor scenes, so were they encouraged to decoupage cutouts onto household objects. Lord Byron is said to have worked on one decoupage screen -- a room-divider common in young single men's lodgings to separate public and private areas -- for three years before he was satisfied with it.
Craft suppliers have printed art on paper specifically for use in decoupage, or you can find interesting art in old storybooks, gift-wrapping paper or greeting cards. Magazine covers are potential sources of art, but if the paper is thin, there is a risk that the advertising on the opposite side will show through once the art has been dampened with the varnish or glue.
If you want your item painted or finished (such as antiqued or varnished with a crackling varnish), do this first. Only when the item is clean and dry should you begin to apply the printed art.
Usually the goal is to present the effect of intricately hand-painted art, so the picture or pictures you are going to apply to the object must be carefully cut out of the background they are printed on. Use very short, very sharp scissors, and turn the paper as you cut, rather than move your hand, for more control over the cut. White space or background color should be neatly trimmed away so that the picture object stands alone.
When you have your art cut, place it dry on the object to be decorated, to find the optimum position. Once you are happy with the placement, brush a thin layer of craft glue (white glue such as Elmer's) or special-purpose decoupage varnish onto the back of the art and smooth it carefully down onto the surface. Press and smooth from the center of the art to the edge, smoothing out any wrinkles or air bubbles that you might have trapped under the paper. Now let the piece dry.
After the glue has dried, you begin to apply layers and layers of varnish. You can use regular wood varnish or purchase decoupage varnish for this purpose. You must allow the piece to dry between layers, and build up a number of layers of varnish, sanding over the art (carefully!) between layers. Art on thin paper is preferable here, since if you use a thick greeting card picture, you will have to build up quite a number of layers of varnish before you can achieve a smooth shiny surface with no visible 'bump' where the cutout begins. This can take quite a while, so you can see how it could have taken Lord Byron three years to complete one screen.
Many people have moved away from the 'hand-painted' look and incorporate feathers, ribbon, buttons and other objects in their decoupage. Truly, it is a craft limited only by imagination.