I feel more comfortable disconnecting a picnic tap after use. They are plastic, and cheaper than the stainless faucets, etc, so I trust them less. I'm sure others out there may disagree, and they leave theirs connected.
Regardless of that decision, I always keep a spray bottle with sanitizer around, so I can quickly sanitize anything that needs to be sanitized. I suggest you do the same. Whether you choose to disconnect or not, squirting the sanitizer into the faucet opening and the connection post is quick and a good habit to get into.
As far as how to clean it, you can do several things:
1) use co2 to push cleaner then sanitizer through.
2) simply soak it in a bucket. Be sure to open the valve, and disconnect the ball lock connector so the solution gets into the line. Again, first cleaner (PBW or unscented OxyClean, or BLC), then sanitizer.
3) get one of those hand pump things or an electric pump and pump the solutions through.