I've been wanting to do the engine bay and under the hood but I am too chicken. :frown:
Don't be!
It's really quite simple. All you need are 3 things: A good degreaser, a good brush, and common sense. (of course also water, MF towels, etc.)
Start off with a cool engine, grab your hose with the sprayer attachment and put it on "shower" or "center". Then get everything wet, moving the hose rapidly to keep the from the water saturating one area, and possibly damaging something. The idea is to just get everything wet.. not try and loosen dirt. That's what the degreaser and brush is for.
Next: spray on a GOOD degreaser, I personally use a combination of P21S TAW and Meg's APC+. Once you spray it on.. let it dwell for a few minutes. Then grab yourself a good boars hair brush (i prefer the swissvax brush), and start agitating the dirt. Every so often, rinse off the brush to keep it clean. Once you are satisfied with the agitation and it's starting to look clean start to spray it down.
Next: Using the same method, spray down the engine bay using the "shower" or "center" position, but don't keep it in one area too long for fear of over-saturation. Once everything is rinsed off start to blot dry everything you can reach.
Next: Admire your new and clean engine bay. It looks good.. doesn't it!!
Optional: A good dressing goes a long way with an engine bay. The key is to find one that leaves a very nice satin finish. I personally use two products: Meguiars HpyerDressing diluted 3:1 (satin finish) and 303 Aerospace Protectant. The idea behind the dressing is to add a little bit of spice.. which is what the Meg's does. But 303's product goes a step further and conditions the plastics, as well as protect them. It reduces the static cling of the plastics, therefore reducing the amount of dust it attracts.
Cleaning an engine bay is quite fool proof under these circumstances: Do NOT use high pressure.. that's a CEL waiting to happen. Steer clear of the alternator, coil packs, abs for obvious reasons (they can get wet, just don't saturate them). And lastly.. do it while it's cool. Some believe it should be warm. I disagree for the safety of your hands, as well as it reduces potential water spotting on the paint around the engine.
Good luck, post back when you get it cleaned up!!