Painting cabinet hinges is a simple process.
Carefully remove the hinges from the cabinet and gently scrape any visible hunks of built-up paint or varnish out of the crevices in the hinges. Put the hinges in a slow cooker, submerged in soapy dishwater, and cook them on high-heat overnight. Gently scrape the old paint off, and then sand the hinges to rough up the surface a bit.
Use spray-on metal primer and paint. Apply a thin coat of primer, then let it dry completely before applying a generous coat of paint. When completely dry, the hinges can be re-installed in the cabinets.