Here's what I do (not sure if it's the best option but it's never failed for me.)
After all the wort has been chilled and and the carboys have been tucked away, I take all my fittings and parts and let them soak in warm water with powdered brewery cleaner. I let my plate chiller soak with my fittings as well. After an overnight soak I hook my hose up to the plate chiller with a jumper hose into the wort in side and turn the nozzle full blast. I let it run for about 5 minutes or more but it may be overkill. The bulk of the residue gets flushed out quick.
If you flush it right away you probably don't need to let it soak in anything, just don't let the hop residue dry out and crust up on the inside, that's when it gets ridiculous to clean.
Anyway, this is how I do it, I don't know if it's the "proper" method but it works very well for me.