i usually dont bother washing the parts while their on the tree, coz they still have to prepped and handled... i was my kits when all the construction is done ( or as much as possible), and then wash it out.... to clean the kits i have a film conatainer full of liquid soap. i use a large flat brush, dunk it in da soap, then work it over them model, then i rinse it off with warm water (not too hot!!) while still working it with the brush, to help get the soap off.... i then shake off any excess water, then place it in my drying box to air dry....
i avoid using a towel or something similar, coz this will place dust, lint, fibers, whatever! :) on the model.... if ur in a hurry, use a hairdryer or ur airbrush too speed it up.....
hope this helps!!!