This is how I clean an engine bay, had no problems in 20 years!
1. First of all is it diesel or petrol - common sense here lads, if petrol, do not aim the water at the coil packs or similar sensitive electrical parts, if you want you can cover electrical parts with silver foil / plastic bags?. Diesel engines are much safer to clean.
2. You will be using a good " all purpose cleaner ", eg Autosmart G101, Megs APC or similar. These cleaners will strip wax, so if the engine bay is really bad cover windscreen and other body panels, this will stop any over spray going on them. DO NOT USE HOUSEHOLD CLEANING PRODUCTS! most of them contain ammonia etc, not good!
3. I always leave one door open so i can gain access to the car, and Safety first, be carefull of moving parts, drive belts etc.
4. Start car and get engine warm / up and running. Turn off and spray entire bay with your APC of choice, leave to dwell for 15 mins or so, make a cup of tea?
5. If required you can use a soft detailing brush for cleaning those nooks and crevices that are hard to get at.
6. Start the engine, - now using your pressure washer, clean the entire engine bay, as said, use your common sense, dont direct the water for a prolonged period at electrical parts.
7. Repeat if your not satisfied its clean.
8. Tip - dont wet the under bonnet felt, they take ages to dry as they soak up water like a sponge. If the felt is really grubby, and you need to use the pressure washer, cover the engine bay, and treat it as a seperate task.
9. Drying - you can either stop the engine and wipe down, or leave engine running and blow off the excess water, or leave engine running and close the bonnet down, the heat generated will soon dry it off.
10. Once clean and dry its time to dress the engine with your dressing of choice. I mainly use Autosmart Finish, simply spray all over and leave, thats it. It drys to a nice satin finish and is safe to use all over on all plastic and rubber trim. 303 Aerospace is also very good but more expensive. Alternatively you could use WD40 i suppose or similar?