Step 1: Meet the mortise lock and door knobs.
Notice the set screw on the base of the knob on the right. This screw should hold the knob securely to the spindle when you turn the knob.
Step 2: What's a spindle?
If the set screws become lose they will allow the knob to turn without actuating the lock mechanism. If your knob is "slipping" try tightening this screw.
Prolonged use with a lose set screw can damage the spindle. If tightening the set screw does not help, you should be able to buy a new spindle at your local hardware store (not the chain with the 16 year old clerk, find the one with the proprietor who is approximately as old as your home).
Step 3: Loosen the set screw.
Step 4: Remove a knob from the spindle.
Step 5: Remove the spindle from the door.
If you need to replace the spindle loosen the set screw on this knob, and unscrew the spindle from the knob to remove it.
Reverse your steps from this point to install the new spindle.
Step 6: Free the lock face from any paint.
If there is paint on the lock face, then when you remove the mechanism the paint may stick to the lock face and peal off the wood of the door.