Open the door partially and stand on the inside of the door.
Push the edge of a flat-head screwdriver into the slot on the side of the inside door knob shank. Slide the inside doorknob off. This exposes the cylinder barrel.
Install a Phillips driver bit into a power drill. Locate the two screws on the face of the plate at the base of the inside doorknob.
Put the power drill in reverse and extract the two screws from the plate. The screws are usually long, so make sure that you unscrew them completely. Pull the knob and plate off the door.
Pull the outside doorknob off and, along with it, the attached cylinder. The outside doorknob is not attached by screws and will come off easily.