Qualities that make high-gloss enamel a good surface cover also hamper efforts to repaint it. The issue is adhesion -- the ability of a coat of paint to stick to a surface. Preparation for repainting needs to be focused on increasing the adhesion capacity of this hard, slick paint.
Since high-gloss enamel repels grease and dirt, the surface accumulation of both must be removed before repainting. Use water, liquid or powdered detergent and elbow grease to remove surface dirt. A plastic scrubber or steel wool for stubborn accumulations removes dirt and also roughens the paint surface slightly. Rinse surfaces thoroughly and let them dry thoroughly, overnight or for 24 hours.
Thorough sanding, although time consuming, is critical for creating a surface that will hold a new coat of paint. Medium-fine-grit sandpaper should be adequate for the job. Wipe down surfaces to remove sanding dust or use a vacuum cleaner.
Although not all professionals or paint companies agree, using paint with the same base as the previous coat maximizes the sticking power of the new paint. That means oil over oil, latex over latex. Substantial technological steps allow considerable crossover between coats of oil and latex paint, but staying within the same base will likely improve adhesion.
Professionals and manufacturers both warn about scraping or sanding high-gloss paint if it is old. Paint applied before 1978 may contain quantities of lead, which requires professional removal. If you believe paint might be that old or leftovers were used later for patching, contact your local environmental protection office for directions on lead abatement. Lead paint in any form is dangerous to humans.