Spray all the parts with de-greaser then agitate with a small brush, wipe all parts down thoroughly until clean with warm soapy water, dry all areas, polish any metals i.e aircon pipes etc, treat all rubber hoses and plastics with rubber and plastic restorer, use carpet cleaner on the carpet at the back of the engine bay and give it a scrub then a hoover, then give it a last spray over and wipe down with a quick detailer.
This may not be the correct method but it works well for me.