Yes, may seem obvious, but did you actually get the cable and plug it in!
Are the LEDs in the right position?
Positive long leg should connect to a pin on the Arduino. Negative short leg should connect to ground.
Are you using the correct pins on the Arduino?
You could be one pin away! Count out if needed and make sure it is really the GND pin that is connecting to the short end of the LED for example.
Are you on the right row on the breadboard?
Easy to be one away - check the 2 legs of the LED/piezo buzzer, check all the wires coming to the resistor etc. Remember only the 5 holes in the row are connected, electricity will not jump from one row to another!
Are all items well connected? In the right position?
Check the resistor, it may have a bent leg and be one row away. Check the wires are really plugged all the way in.
Did you upload the right code for the project?
The LEDs and buzzer will not work unless they are turned on in the code. The Arduino is running code from the person who used it last, make sure you upload the right code to it.
Did you change the code so it will not work any longer?
While experimenting with the code, did you change the pin number or remove a DigitalWrite instruction - if your code is telling the LED to not light up, it will not light up! The circuit does what the code tells it to do.