Hold a straight edge across the top of the face of the cabinet next to the wall where the filler strip will be installed. Slide the straight edge over until it makes contact with the wall. Make a pencil mark on the wall at this point. Hold the straight edge across the face of the lower side of the cabinet and make a mark on the wall in the same manner.
Measure back horizontally 3/4 inch -- usually the thickness of filler strips -- on the marks you just made on the wall, and make pencil marks at these points. Hold a straight edge on the wall next to the marks, and draw a line to indicate the position for a cleat to screw the filler strip to. Note that making the line 3/4 inch back will ensure that the filler strip will be flush with the face of the cabinet.
Use a 1-by-2-inch piece of lumber as a cleat. Cut the cleat to a length that is equal to the height of the face of the cabinet. Hold the cleat to the horizontal line on the wall. Screw the cleat to the wall using 2-inch wood screws driven in with a Phillips bit installed into a power drill.
Measure the width of the gap between the wall and the edge of the cabinet where the filler strip will be installed. Rip the filler strip to this width with a circular saw or a table saw.
Hold the strip in position over the cleat. Ensure the edge of the strip is flush with the wall and the edge of the cabinet. Drill 1/8-inch diameter pilot holes through the strip over the cleat. Drive in 1-1/2-inch wood screws to secure the strip to the cleat.
Drill 1/8-inch diameter pilot holes through the edge of the cabinet and into the edge of the strip. Insert 1-1/2-inch wood screws through the holes, and tighten them with a power drill.