A collage is the assemblage of different forms, creating a new whole.
For example, an artistic collage work may include newspaper clippings, ribbons, bits of colored or hand-made papers, photographs, etc., glued to a solid support or canvas.
Decoupage is a type of collage that is usually defined as a craft. It is the process of placing a picture onto an object for decouration. Often decoupage causes the picture to appear to have depth and looks as if it had been painted on the object. The basic process is of glueing (or using some other form of adhesive) a picture to something you wish to decourate and that adding copies of the ficture on top. As you ad on more copies of the picture you progressively cut out more and more of the background so that, in the end result, the picture has obtained some depth. Often the picture is then coated with varnish or some other sealent for protection.
(Collage is sometimes distinguished from photomontage, a collage made out of various photographs or parts of photographs.)
Surrealism has made extensive use of the collage. Inimage is a name given by René Passerson to a style of surrealist collage (though there may, technically, be an argument as to whether it really qualifies as a collage) in which parts are cut away from an existing image to "reveal" another. Collages produced using a similar or perhaps identical method are called etrécissements by Richard Genovese from a method first explored by Marcel Mariën. Genovese has also introduced the "excavation" collage which is the layering of printed images, loosely affixed at the corners and then tearing away bits of the upper layer to reveal images from underneath, thereby introducing a new 'collage' of images. Penelope Rosemont invented some methods of surrealist collage, the prehensilhouette and the landscapade.
Reference: Etrécissements by Richard Genovese