So I've been trying to take out a sticky door knob to give it some grease and tigthen up the loose jiggles, but I can't figure out how to remove the full knob. I removed the end bit and don't know how to remove the plate and the shaft. I wedged a screwdriver underneath the plate, but that didn't pop it off and I'm hesitant to apply more force.
There's a tool provided with the lockset that engages the heavy ring just inside the finished escutcheon. You can see the two opposing slots on the outer edge. The tool looks like a skinny metal shot glass with two tabs protruding straight out from the cup lip. You'd fit it over the shaft, engage the slots, and turn.
You can try poking the points of a needle-nose plier in there and spinning it out counter-clockwise.
It may be just a pressure fit, I.E. just snapped on. There may be a small slot on the under side of it that will allow you to get a small flat head screwdriver in and pry it off. If so this will expose the screws that hold the rest of the unit together.