Using a machine polisher and a heavy polishing pad (in this case a wool pad), apply heavy polishing compound to the polishing pad in an X pattern.

If using a rotary polisher as depicted, use the medium speed setting to work the polish into the paint, make sure to cover the entire sanded area.

If using a random orbital polisher (also known as a DA or "dual action" polisher), use the highest speed setting.

Be sure to keep the polisher level, and moving. Don't keep it in one spot. Polish even beyond the sanded area.