First do it with a cool engine; i´ve cleaned my own engines for a long time, and what i do is first disconnect the baterry, (+ or both and isolate the + in the batt with a plastic bag or something), then with a moist rag (with water or soapy water) y clean all the dust and superficial dirt, after that, i clean all of the engine surroundings (the firewall, and every sheet of visible painted metal) with some soft surface cleaner like windex and a moist rag, after that, y use another rag with a bit of gasoline in it, to cut through the hardest grease layers in the intake, covers, block, steering and brake system, etc. I also have an old tooth brush and tooth picks, to work certain spots.
After all that, use another batch of soapy water, and rinse everything with clean water and a rag (wetting the rag, not spraying or hosing it down)
Maybe you will need a couple or more washes, but it will do the trick. It takes a while, but i kindda like doing it as relaxation therapy hehehe... also if you used the gasoline, wait for it to evaporate before reconnecting the battery.
Once i used one of those special autozone engine bay degreasers, but it ate through some of my plastics, but other guys seem to have great succes, it might depend on how dry are the plastics.
Also i dont trust karchers or water compressors, since they can get water in certain places you don´t want to have it, even more if your engine has a certain amount of miles on it, it might even disconnect cables and mess lot of things.
But.... if you use them, you need to cover the big black fuse electrical distribution box, the air intake and computer modules (i think the location of those and suggestions are on the owner manual. Water compressors do a good fast job, but once they messed my car up (even using the presure and power specifications for engine cleaning in the instructions), so i don´t like using them.
If your engine plastics are in good shape, you can cover the parts mentioned before with plastic bags, spray the special degreasers, wait the indicated time, and rinse it down with the hose, and scrub the stubborn spots.
Hope this helps.