Mow the lawn near to the fence line and remove any debris from the bottom of the fence. This allows you to easily get at the fence's base in order to paint it fully.
Scrape off all of the old peeling paint using a paint scraper. Leaving any old paint on will compromise the new layer of fresh paint. The paint can also be blasted off using a high-powered pressure washer.
Wash the fence using soapy water and a rough scrubber. This is to remove any dirt, mold or moss that has not been removed with the paint scraping. A pressure washer can also be used if one is available. Allow the fence to fully dry overnight before moving onto the painting.
Lay newspaper or a tarp at the foot of the fence line and, if possible, slip it underneath. This helps to avoid getting dirt in the bristles of the paintbrushes while painting the bottom of the fence.
Paint the front of each fence slat with a large paintbrush. Paint the fence in sections so that you can fully cover an area and not have to come back to it. Once one side of the fence section is done, paint the reverse.
Paint the edges of each section before moving on, using a smaller brush. Also paint any smaller or more intricate areas of the fence at this time.