When stopped, you'll tend to always put the same foot down and leave one clipped. For me, I unclip my left foot. And in preparation to take off, my right foot and pedal are just over the top of the pedal stroke to get the maximum push when I launch.
The catch, at least for me, is to get my left foot off the ground ASAP and get in contact with the pedal before the left pedal comes up over the top of the pedal stroke. Up until that point, the heavier back end of the pedal should be hanging below and slightly behind the spindle. And if you can get your foot up to the left pedal before the down-stroke, where the heavier back end of the pedal starts wanting to swing over the top, and around and around, it's just a matter of sliding your cleat over the spindle and down into clip position.
All of this obviously means gear choice is a big deal when stopping. If you have it in too easy of a gear, there's no way you'll be able to get your foot off the ground onto the pedal before it's on the down-stroke. On the other side, if you're in too hard of a gear, you may not get enough momentum with the first push to go anywhere.