I just cleaned my engine bay yesterday.
I would recommend cleaning things by hand most of the time.
However, sometimes you just want to do a quick immaculate cleaning.
Get some degreaser and spray it in the engine bay, don't spray a lot. Also, don't hit hoses intentionally, if they're dirty spray a little on there if you like just make sure you spray it all off within 2-3 minutes which you should do regardless of whether you sprayed any hoses.
To spray it off, if you don't have a power washer which is what I use its great cause you can really get everything quickly without getting massive pools of water because its spraying rapidly instead of just streaming. Obviously though do NOT get to close with the power washer or you'll probably run into disaster (to close being like 1/2" away from sensitive areas). But not everyone has a power hose (i'd recommend going to a place that lets you use it for like $2 lol) but you can use a garden hose too just make sure you have a spray nosel on it cause again you don't want to stream huge pools of water in there what a mess.
Then dry stuff by hand, don't let it just sit in there and rust for christ sake I've seen so many people do that. Why would you want water pooled up inside there?... lol its not like it just rained with the hood down thats different.
and your engine bay should be well... clean?
and if you're saying what the heck degreasers should I use?
#1 Do not use any high acidity degreasers You WILL KILL HOSES! and PAINT!@
#2 I have some pretty light degreaser at work that is used to get bugs off of bumpers with ease, works wonders, I use that. If you don't have something like that I would reccomend dish soap, but be nice to your car I'd try diluting it first just put some in a spray bottle put water in there and spray away. if it doesn't work very well put more in the bottle and try again.
for drying, just dry it with a rag.
Now its still probably going to look not quite new because plastic gets old and looks like old tires do, what I recommend is using a obviously non flamable tire dressing. You don't want anything in there thats going to emit self igniting fumes. lol
I have stuff that works great at work, I'll update this with the name and some pictures.
Hell maybe I'll just make a little thread.