Remove all the cabinet hardware with a screwdriver, including the hinges. Lay out the doors in your work area.
Remove the old laminate by pushing a putty knife under the loose areas and gradually prying and working it off. Keep the laminate sheets whole as much as possible; this will make them easier to take off.
Sand each exposed door with a vibrating sander, getting it flat and clean. Wipe up the dust.
Measure the first door of the cabinet along the length and width. Mark the dimensions on a piece of laminate, using a square and a pencil. Make the marked area about an inch bigger all around than the actual door.
Cut out the laminate along the lines with a utility knife. Peel off the wax paper backing. Press the laminate onto the cabinet door, letting it overhang by an inch all around.
Run a roller over the laminate to set it firmly.
Cut off the overhanging portions of the laminate with a utility knife, running it along the edges of the door.
Repeat for each door. Reassemble the cabinet.