Open the cabinet doors and examine the screws in the hinges. If they are clogged with paint, you'll have to remove the paint before you can unscrew the hinge. Insert a toothpick into the screw's head and wiggle it back and forth to scrape out paint flakes. If the paint won't come out, dip a cotton swab in paint stripper and dab it on the screw's head. Wait for two to three minutes and use the toothpick again to pry out the softened paint. Avoid getting stripper on other parts of the hinges unless you wish to repaint them.
Insert the screwdriver directly into the top of the screws that hold the hinges in place.
Turn the screws until they are loose enough to pull out. Remove the screws from the hinges.
Remove the cabinet door from the hinges and set it down.
Remove the hinges from the door and set them aside as well.