Fold the afghan length-wise to form a rectangular shape, if applicable. Some afghans are small enough that they will not require folding for display purposes. Have someone help you if necessary so all the corners meet and the fold is even.
Remove all pillows and other materials from the sofa. Lie the afghan across the sofa back. The folded section of the afghan should go behind the couch, if applicable. Work the afghan as needed so it covers as much of the sofa back as you would like in an even fashion. Also drape it so some of the afghan falls over and down the back section of the sofa that faces the wall, which will prevent the afghan from falling off the couch and onto the couch cushions because of people sitting and moving on the sofa. While the afghan will probably slide down your sofa over time, draping it so it has some weight on either side of the sofa back will make this happen less frequently.
Place throw pillows back on your sofa as desired. Have some pillows partially hidden by the afghan and display others over the afghan, particularly those that match the color scheme of the afghan you have chosen to display. Fold the top corner sections of the afghan in, or leave them as is.