For an in depth look at how to remove this type of hardware, and how to clean its innards, I suggest this instructable:
The short version is:
1) Use the knife to carefully cut the paint along the edge of the escutcheon plates. This prevents large portions of the paint from coming with your plate.
2) If needed, use the knife to remove paint from the screw heads on the knob and plate - just enough the get the screwdriver in. The pin may also help.
3) Loosen the screw on the knob and screw the knob off the spindle.
4) Remove the spindle
5) Remove your plates