Clean the walls behind your counter, sink or stove with a degreaser spray and a wet rag to remove any grime, grease or dust that may have accumulated. Wet a rag with clean water and wipe down the walls.
Examine your walls. For your stainless steel backsplash to look smooth, your walls will have to be smooth before applying contact paper. If necessary, fill cracks and holes with joint compound and sand down bumps and imperfections. Wipe the walls clean with a rag to remove dust.
Prime your walls with a latex primer/sealer if you had to repair them with joint compound or if the drywall is unfinished.
Measure the width and length of your backsplash. Add an inch to each measurement for overhang.
Roll out stainless steel contact paper on a clean surface, back side up. Measure and cut the paper to the size you calculated.
Peel the backing from the contact paper on one edge. Pull it back about 3 inches from the edge. Line up the edge with the wall where your backsplash will begin and press that edge to the wall. Make sure to line it up so it is straight.
Grasp the backing from behind the contact paper and begin peeling it off slowly. As you peel off the backing from behind, smooth the contact paper along the wall with your hand, pushing out air bubbles and wrinkles as you go.
Trim the overhang on the edges with a utility knife so they are straight. Use a 6-inch drywall knife and hold the paper down. Cut across with the utility knife, using the drywall knife as a guide to get a straight edge.
Polish the stainless steel contact paper with a soft, dry cloth.