how do gas turbines produce electrical energy?

Answer 1

A gas turnbine operates under the same principle as a steam turbine. The difference is obvious.

But to answer your question..An inert gas at high temp and high pressure causes the turbine to spin. Directly or indirectly, this kinetic energy cause magnets to spin in a magnetic field, producing electricity.

There is a good deal more science involved. I highly suggest checking out http://en.wikipedia.org/wiki/Turbo-electric

Answer 2

The turbine shaft is connected to a large generator.