The cheap way....... with the engine COLD, use an old paint brush and some white spirit to work into the ingrained grime. Don't stint the white spirit, you want it to soak into the gunge that's ingrained in the unpolished alloy.
Let it sit for a while, to get it well soaked into the gunge - 20 - 30 minutes or so - but don't let it dry out.
Using some neat washing - up liquid and that old paint brush again, work it in to get all the dirt mobile and dripping off. Once you're happy, wash it off with some water, make sure you get rid of all the white spirit and detergent - but don't hose it, electrics don't like it! (and it's a good idea to mop up any excess with some kitchen towel or similar).
Start er' up with the bonnet open, and let it warm up till there's no water left sitting about. (it'll probably steam a bit)
If you want to polish the alloy up, little brass or stainless steel wire brushes are good on the as - cast stuff, Solvol Autosol for the polished bits.
Bad things to do:
1. Wash it off with a high pressure hose - you'll get water into lots of electrical bits.
2. Wash it off with a pressure washer - you'll get more water into lots of electrical bits, and into mechanical bits too, in behind oil seals etc.
3. Use a steam cleaner - as above, and you could cook some plastics and electrics as well!
And if you're worried about the flammability of white spirit, check how easy it is to set fire to Gunk - it's just another flammable solvent! (you can't buy a gallon of Gunk for a fiver though!)