Simple transistor switching circuit
What should I do to the circuit so that the LED is lit



Ditch it and start over.

This circuit makes no sense at all.  You have a transistor that is either clamping the voltage across the LED or leaving it open.  Neither will light the LED.

You can use a NPN transistor as a switch to either light a LED or not.  The conceptually simple way is to use the transistor in common emitter configuration:



When the input voltage at the left end of R1 is ground, the transistor is off.  This leaves the bottom end of R2 floating, which prevents current from flowing thru the LED, which keeps it off.

When the input is raised to 5 V, there will be about 1 mA of current into the base.  That will turn on the transistor.  Assuming a typical green LED that drops about 2.1 V, and leaving 200 mV for the C-E drop of the transistor in saturation, that leaves 2.7 V across R2.  By Ohm's law we know that means 18 mA will flow.  That will light the LED nicely, but safely within the 20 mA maximum for a typical LED.

In this case, the transistor is required to have a gain of at least 18.  Just about any small signal NPN transistor can easily be counted on to exceed a gain of 18 at this operating point.