You connect one end the resistor to the arduino pin output you want to use for output. You then attach the anode of the LED to the free end of the resistor and the cathode to ground.
You then connect one wire from the push button to the arduino pin you want to use as your input and connect the other wire to ground. be sure to enable the internal pull up resistor in your software.
One way of attaching the wires is through soldering them together, another is to use solder-less bread board.