How Do You Realise A Not Gate (logic Gate) Using A Transistor?

For example using a 2n2222 transistor: Connect a resistor (1k) between Vcc and the collector of the transistor, connect the Emitter of the transistor directly to the ground; connect a (10K) resistor to the base of the transistor to make the input.  The Collector becomes your output.
Grounding the 10K resistor will let the current flow from the 1k resistor to the output and connecting the input to the Vcc will ground the output through the transistor.
                   10K
Input---------/\/\/\/--------|
                                  __|__       1k
Ground  ______E_/     \_C_/\/\/\/\----------Vcc
                                            |
                                            |
                                            Output

NOT Gate is as similar as a Switch Circuit using Transistor with the necessary biasing!