Measure the face you intend to veneer and cut out a piece of veneer 1/2 inch larger on all sides using a utility knife with a sharp blade. Sand the face of the veneer install area with 150-grit sandpaper. Wipe the dust from the surface with a tack cloth.
Turn your iron on to its highest setting and allow it to heat until a drop of water sizzles when dripped onto the metal base plate. Fit the veneer over the install face so that it overlaps on all sides. Place the iron on top of the veneer. Move the iron across the veneer surface keeping it moving with a slow, steady movement. Allow the glue underneath to soften, you may feel the veneer slide slightly as this happens. Keep it centered so that all edges overlap. Continue ironing the veneer until you have heated the entire surface. For larger pieces, work 16-inch square sections that overlap.
Press the veneer flat with the edge of a wood block, well sanded, so that the edge is slightly rounded. Press firmly, working from the inside out. Scrape along the surface with the block smoothing it onto the mounting surface, pressing the air bubbles out of the veneer so that the adhesive contacts the install surface. Press the veneer firmly around the edges with the edge of the block as well.
Trim the edge of the veneer with the utility knife, pressing against the edge of the install face so that the blade tears the grain smoothly against the edge. Continue around the edges, cutting the excess away until it is all cut off. Sand the edge smooth with 150-grit sandpaper to ensure it will not be snagged, which can cause lifting.