To remove a Kwikset door knob, use a paperclip to press the locking pin that holds the knob and the stem together, and pull the knob out. To remove the entire door knob assembly, remove the knob's inside faceplate, pull out both sides of the knob, and take out the latch plate. Then, tug the assembly away from the door, and take out the strike plate.
To remove only the Kwikset door knob, look for a tiny hole in the sleeve of the knob -- it should be located between the knob's rear side and the door's face. Push a straightened paperclip into the hole until some resistance is felt.
Now, press the piece of metal in a downward direction. This presses the locking pin. To detach the knob, pull it away from the stem.
To remove the entire door knob assembly, keep the door open, and undo the two screws of the inside faceplate with a Phillips screwdriver. Grip the door knob from both sides of the door, and pull both of them simultaneously away from the door to take the parts out.
To detach the latch plate, undo its screws. Then, push in a screwdriver with a flat head between the door and the latch plate, and work it to remove the latter. Grip the assembly with your hands, and pull it away from the door.
Next, identify the two screws that hold the strike plate and the door jamb together. Undo the screws using a Phillips screwdriver to remove the plate.