I'm assuming that the initial contact (from up to 2 blocks away) just tells the restaurant that you're coming and primes their register with your info.
At the restaurant, you order and eat as usual. When it's time to pay (before or after, as per normal at the restuarant) you just give your name instead of cash or credit card, and it's put on your tab. (Which you have to pay later, of course.)
Again, those are assumptions based on what little I've read... Which is probably the same or less than you've read.
It actually charges your credit card right then - the card is kept on file with Square. Just at the moment when the vendor would normally swipe your card, they pick your name and user icon from a list instead.
At the restaurant, you order and eat as usual. When it's time to pay (before or after, as per normal at the restuarant) you just give your name instead of cash or credit card, and it's put on your tab. (Which you have to pay later, of course.)
Again, those are assumptions based on what little I've read... Which is probably the same or less than you've read.