The pushbuttons (like the momentary https://www.sparkfun.com/products/11966 or latching https://www.sparkfun.com/products/11971 ) have an indication of the pinout of the buttons on the side of the plastic molding. One way to test the switch is to use a multimeter turned to the continuity setting. Here are what the pins (not in any particular order associated with the pushbutton's spades):

+ = LED Anode - = LED Cathode C = "Common Ground" NC = Normally Closed NO = Normally Open

One way to light the LED on the metal push button would require you to wire it so that when you press down on the button, the led would light up. You would need 5V to light the LED ring. It can be lit up with a smaller voltage but the LED won't light up as bright.

To connect the battery to the button so that it only lights when the switch is pressed down (momentary or latched), you would connect 5V to the "+" pin on the switch. This is assuming that your system is using the same voltage source that is 5V. Then from the "+" pin, you would wire it to the normally open (NO) pin.

Another wire would be connected from the "-" pin to the C pin. The C pin would essentially be connected to your ground. So as you press down on the button, it would flip the switch and complete the circuit from the normally closed (NC) pin to normally open (NO) pin while lighting the LED ring at the same time. It might be a good idea to use a current limiting resistor (like standard 330Ohm resistor) if you are using 5V directly from your power supply. The LED won't be as bright but you also wouldn't be reducing the life of the LED. I am not sure of the electrical characteristics of the LED that is in the pushbutton.