Unlock the door with the key. With the key still in the hole, insert the end of the wire tool into the hole on the side of the knob. Push down on the tool to release the clip inside the knob. The doorknob and cylinder should now slip off into your hand.
Remove the key and push on the keyhole to dislodge the cylinder from the knob. Remove the retainer ring by prying it off of the cylinder with the retainer ring tool.
Insert the key in the lock again. Turn the key to one side. Push on the keyhole with the plug follower until the cylinder plug comes out the other side. Keep the pins and springs from falling out by pressing the follower tight against the plug as you work.
Push the new cylinder plug into the lock. Attach the retainer ring and slide the cylinder into the doorknob until the keyhole is flush with the front of the knob. Place the knob back on the door and press down until the retaining clip locks it in place.