The circuit diagram is shown below. The seven segment display could have been directly interfaced to the Arduino, but by using the 74HC595, only 3 Arduino pins are used.
The completed breadboard circuit is shown here.
The suggested sequence for building the circuit is:
Insert the 74HC595 IC into the breadboard and hook up its power and ground pins to the top and bottom breadboard rails.
Insert and wire up capacitor C1 (100n).
Insert the 7-segment display.
Insert the 470 ohm resistors.
Wire the resistors to the 7-segment display.
Wire the resistors to the 74HC595 IC.
Wire pin 10 of the IC to 5V.
Wire pin 13 of the IC to GND.
Connect the push button switch and R9.
Wire the switch to the Arduino.
Wire the 74HC595 to the Arduino