For Schlage doorknobs that have a release button on the side of the knob, hold down this button, and pull on the knob to remove it. Other models have a small hole on the side of the knob. Push a pin into the hole, and pull to remove the knob.
In order to remove the rose or escutcheon (the part of the doorknob that attaches it to the door), insert a small flat-tip screwdriver into the slot at the rose or escutcheon's base. Then, gently pull it off of the door's backplate so that it and the door are not damaged.