Walk to the side of the doorknob that has the lock on it. Use a screwdriver to remove the two or three screws from the round base.
Reach around to the opposite side of the door, and pull the knob off that side, which will slide off easily once the screws are removed.
Locate the two screws that hold the latch in place on the edge of the door. Remove each screw, then pull the latch straight out.
Using your new doorknob, insert the latch into the side hole. Ensure that the slanted edge of the latch faces the same direction as the old one, then screw in the latch with the two screws that came with the new doorknob.
Insert the half of the knob without the lock through the hole on the exterior side of the door. Slide the interior knob into the hole on the other side.
Screw the two long screws through the facing of the doorknob. Jiggle the knob to ensure it does not move at all, which means the screws are tight.
Go inside the room, and close the door to make sure the lock clicks into place.