Clean the paneling with a commercially-available water- or solvent-based cleaner/degreaser. Use a scouring pad and go over every inch of the paneling, then wipe it clean. Repeat.
Select an oil-based or pigmented shellac primer or a latex primer. Oil-based and pigmented shellac varieties bond to slick, shiny surfaces like paneling more efficiently than latex, and hide stains better, too. Latex primer also requires a lengthy curing time before it can be painted over. Because oil-based and pigmented shellac contain solvents, however, care must be taken to provide proper ventilation.
Spot-test the paneling with the primer first. Select several 4-by-4-inch spots at various locations in the room. Allow the primer to dry for two days, then evaluate the adhesion of the primer. If adhesion is poor, clean the paneling again and re-test.
Caulk any gaps or holes in the paneling which become conspicuous after painting with primer. Gaps at door and window casings and between baseboards and the paneling are frequent spots, as are gaps where sheets of paneling butt against each other.
Paint with a 1/2-inch nap roller. Properly primed, paneling can be painted with any standard flat, semi-gloss or satin finish interior paint.