How is electricity typically generated?
Electricity is made using a variety of processes:

Electro-magnetic:  This is something that takes mechanical motion and converts it to electricity.  The common way this is done is with a generator that is turned using a steam turbine from a coal or nuclear power plant.  But it could also be a hand-cranked generator, a car alternator, or even one of those "shake to charge" flashlights.

Electro-Chemical:  This is a basic battery-- both rechargable or normal batteries.  The electrical energy is released from a chemical process.

Thermo-electric:  When you get two dissimilar metals and you heat up one side and cool another an electrical current is generated.  I can't possibly explain this one very well so here is the Wikipedia link.

Photovoltaic:  A solar cell.  Converts photons directly into electricity.

Electrostatic:  Basically, using static electricity to do something.  Normally this would be a van de graaff generator.  It is hard, but not impossible, to make something useful with this as an energy source.

Piezoelectric:  Some materials are piezoelectric.  If you strike/hit/vibrate the material it will generate a small electrical current.  This technique is mainly used as a sensor rather than a power source, but there are some places where using it as a power source is becoming practical.

That's all I can think of.  I'm sure there are more, but these are the main ways that electricity is generated.