Just looking through the FAQ, this has been addressed before. Read this thread here:
engine bay cleaning Look at the last post.
I do things differently, but this is certainly a good start. I like to have the engine bay warm (not hot) as it makes it easier to release grime etc.
You will definitely need a high strength degreaser. They reccomended Simple Green, but I would use something like Castrol Superclean (only for the very dirty areas). Otherwise dilute it about 10:1. This will be good for most grime.
Before you do anything, bag off the alternator, distributor cap, and fuse box. They reccomended using a garden hose with low pressure. I wouldn't use that, I used pressure washer, as this has FAR less "volume" of water, but more pressure. I would use a pressure washer. If you only have access to a garden hose use it on the least amount of pressure you can. You DO NOT want to soak anything.
Start by liberally spraying down the engine bay with the degreaser. Making sure you get the grimey areas very well. Make sure you get all angles (ie don't just spray from the front, spray down along the top etc. Let it sit for about 3-4 minutes in the heat of the engine bay (notice I say warm, not I just drove it for an hour hot).
Then crack out the pressure washer, and SPRAY er down. I had to do mine about 2 times to get it to where I wanted. If there are areas that are stubborn, get an old toothbrush and spray degreaser and scrub!
Now that you've got the main areas clean, you can work on details. Get out some metal polish, and polish intake manifolds strut bars etc. Also, if you would like use paint polish on the strut towers, etc.
For all the painted parts, I clean those by hand with "Optimum No Rinse". Make SURE you get the underneath portion of the hood. Nothing looks worse than a clean engine bay but as dirty underside of the hood...
It all depends how much tiem and how anal you want to be.
The LAST thing you want to do is apply a dressing. I use CD2 Engine Bay dressing. It is hard to find, but man this stuff works awesome.
I reccomend Stoners Trim Dressing as well. It's pretty high gloss, so buff it off after letting it sit for a bit. Other than that, that's all there is too it. it's more time consuming than anything.