There are so many things you just got wrong.
(1) Voltages -
For an NPN (silicon) transistor to turn ON the base needs to be at least 0.6V more positive than the emitter.
For a (red) LED to turn ON you need at least 1V8 across it.
The minimum voltage (V2) that needs to supply the base is 0.6 + 1.8 = 2.4V
The voltage at the collector needs to be higher than the base, when fully turned ON this is at least another 0.2 volts so the minimum in this circuit should be 2.6V (V1)
(2) Controlling currents
Your circuit doesn't limit any current. You haven't destroyed the transistor and/or LED because your voltages are too low to do any damage (i.e. its not working). This is bad design.
Adding series resistance will prevent damage due to excessive current as the voltages are increased.
(3) Circuit configuration
The circuit you have used is called an emitter follower it is not using the transistor as a switch. The voltage at the emitter follows the voltage at the base (but about 0.6V less.
A transistor used as a 'switch'
Typical values for R2 would be in the range of a few hundred Ohms to a couple of thousand Ohms depending upon supply voltage. The value of the resistor depends upon the curent needed - more current , smaller value. Typical values for R1 would be in the thousands to tens of thousands of Ohms. (usually about 100 times R2 which assumes a minimum gain of 100 for the transistor).