Open the door halfway so you have access to both the inside and outside door knobs. This also helps prevent accidentally locking yourself in the room.
Remove the screws securing the inner door knob rose plate to the door with a Phillips screwdriver. Once you remove the screws, pull the inside door knob away from the door.
Press a paper clip into the small hole on the neck of the inside door knob, if your door knob has no visible screws. Press inward with the paper clip when you feel the spring, and pull the inside door knob away from the door. Find a notch between the rose plate and the door and pry the rose plate off with a flat-head screwdriver. Remove the two screws securing the mounting plate to the inside of the door with the Phillips screwdriver, and pull the mounting plate away from the door.
Turn the outside door knob left to right. Sometimes loosening all of the securing screws is enough to loosen the square spindle and latch.
Spray some graphite onto the latch mechanism in the seams on both sides of the square spindle.
Rotate the outside door handle to move the latch in and out and distribute the spray graphite into the latch mechanism. Spray more graphite if necessary until the outside door knob turns freely.
Reattach the inside door knob in the reverse order of disassembly.