As you can see here, the LEDs sit inside the button cavity and the two button contacts surround it. This allows for the nice frosted LED effect.
The LEDs are seperately controlled from the buttons - an Arduino or similar is required to read data from the buttons and then write out what LEDs to light up.
Bend the LED legs out so that the LEDs sit nice and flat against the PCB. Flip over the PCB so you can solder them in