The way I do it is pretty close to how theveed does it.

I've found Simple Green, 2 paint brushes, a sponge, a lot of plastic baggies (and elastic tie strings) and a lot of towels work best for me.

Also, engine detailing should be done before you work on the outside of the car (but after an underbody wash, as theveed had suggested).

One thing I've found useful over the years (which I actually picked up from a friend who owns a detailing shop) is to keep the engine running while hosing it down. This way, you can listen to changes in the way the engine sounds while you wash away the dirt from it.

If and when you detect a change in the pitch of the engine while you are hosing it down, stop immediately and take the necessary corrective actions.

Engine detailing is not as hard as it sounds! Good luck, and have fun!