How would I wire this to the pi's GPIO?
One wire to the GPIO pin and the other to the ground pin.
When your program initialises this GPIO pin as an input, you should also specify you want the pull up resistor to be enabled. However if you use GPIO 0 & 1 on the old issue 1 boards or GPIO 2 & 3 on the new issue 2 baords then there is already a hardware pull up resistor fitted so there is no need to enable the internal one. It does no harm if you do however.
Also what kind of signal would this send back to the pi?
A logic level signal. When reading the GPIO pin you will see a logic zero when the button is pushed and a logic one when it is not. These are also called true / false levels in Boolean logic.
Would it send an "on" signal once?
As long as the button is held down it will return a logic zero, it will only read back as a logic one when you release the button.