Black and one of the blue wires to ground. The other blue wire to an Arduino input pin. The red wire to an Arduino output pin.
You don't need a series resistor for the led because the switch has one built in already. Unfortunately, that built in resistor will have been chosen for 12-24V, so the led will be quite dim with only 5V.
If you want the led to be brighter, you will need a higher voltage supply, like 12V, an ordinary npn transistor like bc337 and a current limiting resistor for the transistor base, 1K~4K7
I could see it as follow?:
black wire = led cathode >> arduino ground
Red Wire = Led Anode >> arduino digital pin
blue wire1 =button terminal 1 >> arduino ground
blue wire2 = button terminal 2 >> arduino digital pin
when button is pressed red wire should get +5V from the arduino digital pin and when button is not press that leg should see 0V ?
Yes, that is possible. But if that is what you want, you do not even need an Arduino! You can connect 5V to red, black to blue and other blue to ground.