I want to make a small model of how electricity is created by burning coal. I want to show a model that works and be able to light up and very small light bulb(the ones found in an average school microscope). How would I do this.

You will find this difficult. I would suggest another project. Burning coal causes heat, and commercially this is used to heat water to steam which turns a turbine which turns an electric generator.
This is not something that can be done easily with a model.

So how is electricity used in light bulbs in our homes generated.

The process I described is the way home electricity is generated.

To create a small model of how electricity is generated from burning coal, it would be challenging to achieve the exact process in a small-scale project. However, you can create a simplified model to understand the basic principles involved. Here's a possible approach:

1. Materials needed:
- Small heat source (e.g., candle or small lamp)
- Small turbine (can be built using a small fan blade or propeller)
- Toy generator or motor
- Connecting wires
- Small LED light bulb (as found in an average school microscope)
- Optional: battery pack or power source for the motor/generator

2. Set up the model:
- Place the small heat source (representing coal) at a safe distance from the other components.
- Position the turbine directly above the heat source so that it gets heated by the rising heat.
- Connect the turbine to the motor/generator using wires.
- Connect the LED light bulb to the output of the motor/generator using more wires.
- If using a battery pack or power source, connect it to supply power to the motor/generator.

3. Demonstrate the model:
- Light the heat source, such as a candle or small lamp.
- As the heat rises, the turbine should start spinning due to the hot air flow.
- The spinning motion is transferred through the connected wires to the motor/generator.
- As a result, the motor/generator produces electricity, which powers the light bulb.
- The small light bulb should light up, albeit dimly, to represent the produced electricity from burning coal.

While this model may not accurately represent the complexity of a real power plant, it can help demonstrate the basic concept of converting heat energy into mechanical energy and then into electrical energy. Remember, safety precautions should always be taken when working with heat sources and electrical components.