Usually I just fold mine back behind the iPad, but if I'm going to hold it for extended periods of time, I'll pop the keyboard completely off and set it somewhere safe (like in my Swiss Gear bag where I usually store the iPad itself.)
If I'm going to switch over to my standard Smart Cover, I put the ASK in the box it came in until I'm ready to put it back on the iPad.
For the first time ever, I do have a bit of a dilemma as far as iPad typing--the 10.5" on screen keyboard is so much better size wise than the 9.7" was, I've considered leaving the ASK at home more and more often. For typing quick replies, tweets, posts, etc., the on screen keyboard has been just fine for me. Could not say the same for any iPads I've owned prior.