Insert the key into the lockset. Turn the key 90 degrees counterclockwise, until it is vertical in the key hole.
Look for a small hole in the side of the handle, near the face of the lockset. Insert the end of a door handle tool or small flat-head screwdriver into the hole. Press in on the tool or screwdriver while pulling out on the handle. Slide the handle off the lockset until it butts up against the key.
Turn the key 90 degrees clockwise, and pull it out of the key hole. Pull the handle the rest of the way off the lockset.
Press the tool or screwdriver into the hole on the other handle. You don’t need to insert the key or turn the lock button. Pull the handle off the lockset.
Slide the handle from the side with the key hole over the lockset shaft. Press in on the handle until it locks in place.
Slide the handle from the lock-button side of the lockset onto the shaft until it butts against the retaining clip. Insert the key in the key hole, and turn it 90 degrees counterclockwise. Press in on the handle until it locks in place. Remove the key.