Unfasten the screws below and above the doorknob on the exterior side. The screws are on the base of the doorknob. Unfasten the screws below and above the doorknob on the interior side. The screws are also on the base of the doorknob. You may need to use the flat end of the screwdriver to pry the base of the knobs from the door.
Pull the two doorknobs apart, separating them from the door. Do not remove any other part of the doorknob.
Place the new exterior doorknob over the hole on the door, and fit the original interior doorknob on the other side of the door. Tighten the screws on both of the knob's bases.