You can leave it connected, but if it accidently opens (um, like if someone, not me of course, would accidently drop it on the side of the keg and accidently open the top without noticing........) your keg can literally disappear into the bottom of the fridge! So, either loop up the excess tubing and keep the cobra faucet on top, or keep it off until you're ready.
Anyway, to clean it is easy! See the "slot" on top of the disconnect? Using a flat head screwdriver, take that off. When you do that, there will be four parts. Do it over a white surface (NOT the sink!) so you can see them all. There is a spring, a plastic pin, the top you took off, and a black gasket. The black gasket is really important! It may be around the top you took off, or inside so look carefully and place those pieces in a bowl. Then, you can go over to the sink and unscrew the top of the cobra faucet or just open the faucet and run water and then sanitizer through it. Sanitize the little parts in a bowl, and put the QD back together. Pin first (long side up), then the spring, then the gasket on the top and screw it back on. That's it!