Question

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.