Once a month I do a thorough cleaning. I mix up a 1 gallon solution of BLC & water in a corny keg, and run 1/2 of it through all the lines, shanks, & faucets. I let it sit for 15 minutes in the lines, then remove the faucets, disassemble them, and soak them in the BLC solution that I collected w/ the first flush. Once they've sat for 20-30 minutes I rinse & reinstall them, then flush the remaining BLC solution, followed by about 1/2 gallon of cold water. That takes care of all the lines, shanks, faucets and to some extent, the disconnects.
For ordinary keg swaps, I just run some iodophor solution through everything and skip the water rinse. I disassemble the disconnects (unscrew the top so I can remove the poppet, spring, etc. and soak them in sanitizer) and then let everything drip dry for a minute or two before tapping the new keg.
EDIT- I meant to add, the easiest way to clean a setup w/ a picnic tap is to unscrew the top of the disconnect, removing the spring and poppet, and also unscrew the picnic tap end, removing the valve/handle part. Soak those parts in sanitizer. Then you can run hot water, followed by sanitizer (via gravity) through the lines and the body of the tap and disconnect. Let it sit a minute, then drain it all out, reassemble everything, and you are good to go. I also like to swab down the keg posts w/ sanitizer to make sure that nothing nasty can get into the keg when I reconnect everything.