Open the cabinet doors and examine the hinges that are holding them onto the cabinet. If the doors are held on by European-style hinges (with a large, round part that is countersunk into a large hole on the back of the door), you can remove the doors by unclipping the hinges, then removing the remaining half of the hinge from the cabinet with a screwdriver. With more old-fashioned hinges, you will have to unscrew the hinges from the frame of the cabinet to get the door off.
Test the hinges that go with the Shaker-style doors by holding them up to the screw holes from the old hinges. Cover any old screw holes that won't be covered by the new hinge by filling them with wood filler, allowing it to dry for at least 4 hours, then giving it a light sanding.
Hold the Shaker-style doors up to the cabinet frame so that the hinges are in position. Insert screws into the screw holes in the hinges and screw them in. This task is much easier if you have someone helping you who can hold the cabinet door up while you screw in the hinge.