It won't be quite as simple as your diagram.
The 120V AC won't be good for a transistor. The average transistor would very quickly fry in that situation
Normally you would use a transistor to switch the LED when the thing that should be doing the switching isn't strong enough to power a LED (or many of them) on its own. For example, I might connect a pin of a microcontroller to the transistor which powers the LED because the microcontroller can't provide enough current to power the LED directly. Think of it as an amplifier - a weak input makes a strong output. With 120V AC, you already have a *very* strong input from LEDs perspective.
What are you trying to do? Maybe I can point you in the right direction with more info.