Here is what I do...
on a warm, NOT HOT engine, I will give everything a nice soaking with some Simple Greene. I pay special attention to the alternator, as to not spray on, or around it...keep this in mind for everything you do with liquids around your engine bay.
I will then, with VERY LOW pressure, give the engine a gentle bath with water from a hose. Making sure to get as much of the Simple Green off as I can from everything. You can use some high pressure here and there, as long as your not near any electrical connections as they are sealed...but under pressure not very good.
Let it air dry, I usually let it sit a day if I can, then I use a can of Turtle Way F21 tire shine (in a green can) Give everything a nice good coating of this and just let it sit and dry. This will give your engine bay and all your wire loom and hoses etc. a nice factory new shine, but wont attract the dust.
This is what I do...others may vary. When I detail a persons car, and they want the engine done as well, its such little work and easy money to make the engine bay look like new again.
Sometimes, if there was a leak, and it was or was not fixed, and has dirt build up on it, you might have to bust out the pressure washer and hit that spot good before you begin, as an additional helpful tip.
~F~