One screw at a time! Start looking for screws anywhere you may think that it would make sense to hold them in place. They are usually all around the perimeter. Most of the furniture is built from the inside out, and when they are done a section, they will place a piece of board over where the screws would show, and then staple it down. A hanging cabinet, for example, would have most of the screws hidden between the bottom and inside layers of wood. You would need to remove a layer to get at the screws. This is almost impossible to do without breaking the thin wood as there isn't an easy way to remove the staples. Just some food for thought in case you were planning to re-install them for resale value down the road.
