There are two ways one's quicker than the other but prep first use cling film as mentioned above to cover some electrics sensors etc you can use foil on top of cling film too for added security.
Next use a normal hose or if you got a spray head attachment even better as it's a slow rinse off like a shower then, so rinse first then use a engine cleaner and spray liberally (could use Meguiars, autoglym, Gunk) I tend to do half the engine then repeat. Agitate with a brush then rinse. Repeat the other half. Dry as thoroughly as you can with an old microfiber or cloth, I have a blow dryer which is fantastic for this also. Then make sure you take off the foil and/or cling film.
Other way takes longer but good if your worried about using a hose, get a bucket of water and a few old rags/cloths, because you won't be soaking the engine as long as your careful there will be no need to use cling film unless you want to. Dampen engine with damp cloth, spray your cleaner on, agitate and use a damp cloth to remove, then dry. Again do half at a time.
It's a good idea then to use a engine bay dresser then. Shine's things up and protects a bit making cleaning easier next time. Personally I would avoid a pressure washer just use a normal hose.
So you will basically need:
Hose (Spray attachment if you have one) or bucket of water depending of method.
Plenty of old rags/microfibers/cloths.
Soft wheel brush/detailing brush an old toothbrush is also good for small spaces.
Cleaning product (Meguiars engine cleaner/Autoglym engine cleaner/Gunk engine cleaner) Try and use a water based cleaner.
Engine dresser (Meguiars engine dresser/Autoglym vinyl and rubber care) both good products.
So get your hands dirty and good luck lol.
Should turn out like this, my 2004 EP3