Step 1: Remove loose stuff with hose + brush.
Step 2: Cover everything in sight with copious amounts of vastly expensive engine degreasant. Leave for 5 minutes or so, then scrub hard. Try to remove all of the thick oil deposits in this step. Never mind if the paint doesn't shine yet, just get rid of the oil.
Step 3: Using meths, rub a little bit of paintwork at a time to get the layer of grease off the paint, then remove again with water before the meths eats through the paintwork (as it will if left there..). The paint will look lovely and shiney now, with any luck

Step 4: Polish up anything that's polishable

You can get some kind of engine bay paintwork protector, from Turtlewax or someone I think, leaves some kind of a film over the paintwork to stop grease building up again. Never used it myself, but it's worth a shot if you can find any
Admittedly I did this whilst I had the engine out of the car in bits, and there's a fair bit of paintwork (cylinder head, rocker cover, air box lid, manifolds, heat shroud, various little bits of touching up of the engine bay..), but this is what you can expect to achieve with a bit of elbow grease:
From this:
To this:
Good luck with it
