Removing an interior doorknob is a simple task, but it can be daunting for a beginner---especially when there are no screws visible on the outside of the knob. How can you unscrew something when all its screws are hidden? It's fairly easy, once you know the trick.
Remove the knob itself from one side of the door. The knob is held on by a spring-loaded detent just behind it, on the doorknob's barrel. Pressing this in with the end of the screwdriver will allow you to slide the doorknob all the way off the barrel. Do so.
Pry off the rose of the doorknob---the ring at the base of the barrel that is flush against the door. There may be a notch somewhere along the edge of the rose, for easy removal. Just insert the end of the screwdriver into it and pull outward. If no such notch exists, you will have to pry it loose the hard way. You might not be able to get the tip of the screwdriver under the edge of the rose---use a table knife instead.
With the rose and knob removed, you will be able to see the clamping screws that hold the doorknob together. Unscrew these and pull the spindle loose. Finish by unscrewing and removing the latch assembly.