Unscrew the knobs and remove them. Examine the back of the knobs first to determine if you need a flathead or Phillips screwdriver. Store the screw backings in the drawer so they don't get lost.
Sand the knobs, if necessary, using fine sandpaper.
Cut a piece of cardboard to 1-foot square. Insert the knob screws through the cardboard, spacing them out to give you plenty of room to paint around each knob. Leave a centimeter of space between the knob and cardboard so you can access the entire piece when painting.
Suspend the cardboard between two drinking glasses tall enough that the knobs don't brush the surface you're working on. Tape the cardboard into place. This allows the knobs to sit straight and dry without touching them or without the knobs touching another surface and marring the paint job. You can also use two soup cans, paint cans or any other sturdy object that will hold the weight of the cardboard and knobs.
Prime the knobs, if necessary. Grasp the screw with your other hand underneath the cardboard to hold the knob steady as you paint. Allow the primer to dry completely.
Paint the knobs in the same manner. Push up on the screw to access the entire knob base, but avoid moving the screws too much because this can expand the cardboard hole and allow the knobs to flop over. Allow the paint to dry completely before adding another coat.
Remove the knobs when dry and screw them back into the furniture.