Carefully, with steam and water and rags.
Steam from what?
Hot water.
Duh but you can't boil water under the engine. Well I guess you could dosent sound like a good idea though.. I guess you could use a clothes steamer
I was totally messing with you. Use a steam cleaner. Not always easy to find, but most cities have a spot that will do it.
Hot water.
I did this one time, sprayed the bay down with simple green , let it sit, then used gentle water pressure to rinse everything off....worked well.
For tough built up areas I will use a toothbrush.
When all else fails, Marines break out the toothbrush. Ahh, memories.
Simple GReen works great, but for really dirty and greasy engine bay I use Gunk.