Use of transistor for switching the led
You should not disconnect your powersupply's ground connection with the transistor. The way you draw it the LED is connected to a closed loop that is not really affected by the state of the transistor. 
So schematic wise you're probably looking for something like this.  

Component values give roughly 15 mA LED current. 



Idrive ~= (V2 - Vbe_Q1)/R1 ~= (1.5-0.6)/1000 = 0.9 mA.
I_LED ~= (V1 - V_D1)/R1 = (9-3)/390 = 15 mA.
Use lower value of R1 for more current.