How can I tell which pins I will have left available by looking at a shield?
If you look in the 'Tutorials' section of this page you can see the pins used. All of the buttons come through in one analogue input and you'll need a further 7 digital I/O pins. So 8 in total which would leave 5 analogue and 4 digital (I think) pins on an Uno.

As for how to tell which ones, does it matter in advance? I would just map the I/O in the sketch to suit. If you need to plan that far in advance though, it seems that J5 in this schematic shows which pins travel through the shield (i.e. are available to use in conjunction with the shield). Also J6 shows the 5 remaining analogue pins.