When the engine is cold, I very gently spray car wash soap all over it. I let it set a few minutes and wipe down with a mit the painted metal parts, plastic covers, and fluid reservoirs. I then rinse very gently, followed by blowing dry with a leaf blower. I then drive it for 10-15 minutes to finish the drying. I've done this with every engine I've ever owned. They all look great and you can spot leaks and problems more quickly. I've never had an electrical issue or even a rough idle with any of them, ever. I started this with an 82 Pontiac J2000 and every car since. I've always gotten top dollar when selling them.
Oh, I left out one thing. If there is any gunky grease or oil, I hit that spot with engine degreaser, let it set, and sometimes hit it with an old toothbrush. That always takes care of it. Again, this helps to spot leaky gaskets or hoses.
I've never bothered to cover anything or even plug the air intake. The key is the gentle soaping/rinsing with very little pressure. I use a pressurized yard sprayer for the soapy water application. It essentially mists the soapy water onto everything. I do this usually only once a year. I like to do it in the springtime so as to wash off any road salt that may have sprayed up in there. If doing it a second time, it is usually after some off-roading where mud has splashed up into the engine bay.