Here's how I do a quickie clean-up on customers' cars at the shop:
Spray the nasty part(s) with brake clean (I prefer Brake clean over carb clean because it's usually not flammable - check the can - it will surprise you if a plug wire or coil lights it up - personal experience
)
Start the car and let it warm up about half-way, this will help soften the yucky stuff and also provide some heat to help hasten the drying process afterwards. Shut the engine off and spray liberally with Simple Green - 50%/50%, SG/water - Let sit about 5-10 minutes then blast it with a hose.
Try to not force water into anything, particularly electrical components and stuff like air filters, etc. If you're working with a car that has a distributor you can 'bag it' with a sandwich bag or similar and tape or rubber bands before beginning.
At the shop I use an air hose to give it a quick blow-off, at home I use the outlet blast from the shop vac. If you don't have one use a hair dryer, it'll work, just slower. Leaf blowers are good too, but the neighbors will probably give you funny looks. Pay particular attention to the electrical goodies, blowing the water away from them, not into them. Start the engine and if it runs rough for more than a minute or so shut it off and go back to the drying device you have handy. That's all there is to it!
p.s. I recommend doing this at home rather than a car wash, at least until you've got the hang of it. There's nothing like the added frustration of being stranded at the car wash, by your own doing, with people waiting behind you to use the bay. I don't even like doing it there unless I know the car well.