My engine bay wasn't touched for a good 75k miles - it was downright disgusting. Now people compliment me all the time on how new it looks underneath.
First time I cleaned it all I did was wrap the fuse box and relays, airfilter, alternator, and coil packs in plastic bags. I ran water over everything (just low pressure hose water) and then sprayed it down with Orange Clean (Simple Green is what I wanted to use, but I just ran out). I let it sit in the shade for about 20 minutes. Then I took the hose again with low pressure, and just rinsed everything off. I sloshed away most of the water with a towel and then let the motor sit in the sun for the rest to dry up quickly.
The next step is what is different from most. I've never heard of anyone else using my technique before. I bought this Meguire's Exterior detail spray stuff. It's in a bigass aerosol can and it sprays almost like a fog/mist. I unloaded the can on the dry bay and then just smoothed everything out with one microfiber towel.
My engine bay will stay spotless for weeks, then all it takes is a dusting. I reapply the detail spray about every 3-4 months. I havn't recleaned the bay in over a year and it still looks superb.