Depends on how grimey it is. Dusty dirt is no problem and easily cleaned but if there is grease / oil then I change my approach.
Many different good products remove "general" dirt and light oil (Simple Green, Meguires APC+, etc.). Heavy grease and oil may need a stronger product.
I work on a cool engine only. Place newspaper on windshield and over wipers. I usually cover the alternator (and distributor is present) in aluminum foil. Hose down with water, not too stong of a spray. Spray on cleaner and use assortment of brushes to aggitate, then rinse WELL. (I have and do use a pressure washer, set to WIDE pattern, held 2 feet away, but ONLY on dusty engines, i.e., not oily or greasy engines.)
Remove foil shields and hand clean those areas that were covered.
I use a leaf blower to dry the engine and remove pools of water.
Remove overspray from painted surfaces.
Once dry there are many "dressing" products you can use. I found Stoner Trim Shine to work as well as (or better than) the expensive stuff and better than most other otc products. Spray everything to coat but not so much as to cause much dripping/running. Allow to dry.
Remove paper coving from windshield and wiper cowl areas.
This engine (below) had 112,000 miles when pics were taken.
Regards,
GEWB