Thoroughly clean the paneling before it ever touches paint. Use a water-based cleaner designed to cut through grease in order to remove any oils and dirt present on the paneling. After rinsing the wall, wash it once more for good measure, then allow the surface to dry completely before moving forward.
Fill the ridge between the each plank with joint compound to disguise paneling as dry wall, unless it is made of solid wood. (Wood shrinks and expands, so filler will not last.) Once the compound is dry, sand the ridge and the rest of the panel to create a level surface.
Apply a coat of primer to the paneling with a paint roller. Oil-based or shellac primers will cure more quickly than latex primer, which may take up to a month to cure completely. Oil-based and shellac primers are also more forgiving of walls that may have some oil or dirt remnants. Allow the primer to dry completely per the manufacturer's instructions before you paint over it.
Cover the paneling with your paint color of choice using a paint roller. According to "This Old House," latex paint will adhere to a sanded panel covered with primer. Use a 1/2-inch roller nap to apply the paint. A second coat may be necessary for darker colors. Let the first coat dry completely before you add a second coat--two thin coats are always better than one thick coat.