Remove with a small flat screwdriver the outer “C” ring on the new/replacement exterior key cylinder and pull the cylinder tab out of the center end of the new/replacement exterior key cylinder. Discard both the “C” ring and tab.
Turn the latch on the door to the open position and remove the outer latch plate with a Philips screwdriver. Remove the exterior lock itself. Note whether the interior of the lock is marked with an “R” for right, or “L” for left. It matters later.
Remove the back plate from the lock, without disturbing the interior parts, by unscrewing its three Philips head screws. Look at the large gear, as opposed to the smaller top gear, and note the placement of the “L” and “R.” Pull off the large gear.
Remove the existing key cylinder from its housing and slide in the replacement cylinder. Lubricate the back of the small new/replacement gear and slide it into the slots on the cylinder’s back.
Replace the large gear taking care to position the “R” and “L” in the same places as before.
Re-attach the back plate. Look at the opening on the back plate and verify that an “R” or “L” is visible.
Remount the lock on the door and re-attach the latch plate. Test the lock to ensure that it turns easily when the replacement key is inserted and turned, and that it locks and unlocks completely.