One problem with laminate cabinets is that when the laminate surface gets scratched, dull or faded, you can't refinish it the way you can real wood. Laminate is made with plastic layers, and the only feasible repair is to cover it with new laminate or veneer (thin-cut wood that's often coated in plastic). Peel-and-press veneer kits with removable wax-paper backing is available at your local hardware store. In many cases, it's just the cabinet body that's laminated, with real wood used for the doors and drawer fronts.
Use your screwdriver to remove door hinges from the cabinet. Set the doors aside. Pull out the shelves, drawers and any other removable parts.
Buff the laminated surfaces of the cabinet with a small sander and 100-grit sandpaper to remove the shine and any dirt or grime. The surface shouldn't reflect light when you're done. Clean off the dust.
Use your tape measure to measure each section of the cabinet that's going to be veneered. Transfer the measurements to pieces of veneer. Expand the measurements so the pieces are 1 inch bigger on all sides than the section they're going to.
Cut out the pieces from the back, through the waxed paper, scoring with your utility knife and then snapping the pieces. Keep the waxed paper intact on the cutout pieces.
Hold the first piece of veneer in front of the correct section, overhanging it on all sides. Peel off the top few inches of waxed paper. Press the veneer to the surface (the adhesive should grab immediately).
Peel down the rest of the paper from underneath, while pressing the veneer to the surface. When the whole piece is secured, roll over it with your rolling pin to press it more tightly into place.
Cut off the overhang by running your utility knife along the edge. Repeat the process for each section of the cabinet. Reinstall the door hinges and other hardware.
Use caution when cutting the veneer, keeping the utility knife pointed away from you.