For the Button you'll use USB Overdrive (www.usboverdrive.com ) to map one of the mouse buttons to the enter key.
First go download and install USB Overdrive which will add a pane to System Preferences. Open the System Preferences and go to USB Overdrive. Click on "Any Mouse, Any Application" and select "New Duplicate Settings..." Then select Photo Booth for the application and hit ok.
Now you want to maped the buttons to keys the Photo Booth uses (namely the Return key).
I mapped them like this:
Left Button -> "Do nothing"
Middle Button and Right Button -> "Press Key" and then select "Return" at the bottom
You could map one to the Esc key to use a a cancel button but I feel like that takes away from the photo booth atmosphere. :P
I set the mouse facing "backwards" in front of my external monitor like you can see in the picture. I taped over the bottom of the mouse to keep people from messing with it and I used a little double-stick tape to keep it from sliding around when people pressed the button.