A method used to fasten a doorknob to a spindle without visible screws (using hidden screws to attach the assembly to the door) is called a screwless doorknob.
Screwless doorknobs use an attachment device called a detent that locks the doorknob to an unthreaded spindle. The detent is designed to resist the rotation of the doorknob or handle about the spindle.
A detent is usually a spring activated pin or small thin plate attached to the spindle that protrudes into a notch or hole in the doorknob to prevent rotation.
The assembly is fastened to the door using screws hidden under a cosmetic face plate. Getting to the screws holding the door knob / latch assembly to the door is not intuitive and can be a little tricky.
To remove the doorknob, the detent is depressed via an access hole in the doorknob. The access hole is usually a thin slot shaped hole or a small round hole. With slotted detent access holes, a small flat blade screwdriver is used to depress the detent. With small round detent access holes the end of a wire paper clip can be used to depress the detent. Once depressed, the doorknob may be pulled free of the spindle.
Once the lever is removed the next step is the removal of the decorative door knob trim ring. The trim ring covers the lock set backing plate that holds the doorknob and latch assembly to the door.