Electricity generation - whether from fossil fuels, nuclear, renewable fuels, or other sources - is usually* based on the fact that:

"When magnets are moved near a wire, an electric current is generated in that wire."

In the picture, the shaft and armature (with copper wire) spin around. The magnets are on the outside (they don't move). Electricity, at the "+" and "-" terminals, is shown in the picture as a lighting bolt.

A "generator" and "motor" are essentially the same thing: what you call it depends on whether electricity is going into the unit or coming out of it.

A generator produces electricity. In a generator, something causes the shaft and armature to spin. An electric current is generated, as shown in the picture (lighting bolt).

Lots of things can be used to make a shaft spin - a pinwheel, a crank, a bicycle, a water wheel, a diesel engine, or even a jet engine. They're different sizes but it's the same general idea. It doesn't matter what's used to spin the shaft - the electricity that's produced is the same.

A motor uses electricity. In a motor, the electricity comes in through wires attached to the positive (+) and negative (-) terminals. The electric current causes the armature and shaft to spin. If there's just a little current and it's a small motor, it won't do very much work (i.e. it can only spin a small fan). If it's a large motor and it's using a lot of electricity, it can do a lot of work (i.e. spin a large fan very fast; lift a very heavy load; or whatever the motor is being used for).

Large (Utility-) Scale Electricity Generation

What if the coils are stationary, and the magnets are spinning? That works, too.

An electricity generator has two parts:

1. The armature, also known as the stator, is the stationary part of the generator. It is a hollow cylinder, with coils of wire on the walls of the cylinder. The coils are stationary.
2. The rotor is an electromagnet that rotates inside the stator. The magnets are spinning.

Here's an inside look at one of the two turbine generator units at the Kalaeloa Partners' 180 MW power generation facility.

The rotor has been removed for system maintenance. You can see the coils in the armature. The armature is on the outside and does not rotate. Click on the photo for a larger picture.

Here's the magnet, which rotates.

This is the rotor which was removed from the generator shown above. Click on the photo for a larger picture.

As you can see from the photos above, a commercial utility electric generator can be quite large. Another example is the 180-megawatt generator at the Hawaiian Electric Company's Kahe power plant on Oahu; it is 20 feet in diameter, 50 feet long, and weighs over 50 tons. The rotor spins at 3600 revolutions per minute.

Although the principle is simple (copper wire and magnets), it's not necessarily easy!

Steam turbine generators, gas turbine generators, diesel engine generators, alternate energy systems (except photovoltaics), even nuclear power plants all operate on the same principle - magnets plus copper wire plus motion equals electric current. The electricity produced is the same, regardless of source.

A geothermal power plant is pretty much a steam power plant, since what comes out of the earth is steam. Rainwater soaks into the ground and goes down, down, down...far enough until it reaches a region which is really hot (in Hawaii, that's about 6000 feet). A well is drilled, the steam comes out, goes through a heat exchanger, and spins a turbine... spinning the rotor and generating an electric current. By the time the steam has gone through the heat exchanger, it has cooled off and become warm water. It is then re-injected into the ground.

In a gas turbine power plant, fuels are burned to create hot gases which go through a turbine, which spins...spinning the rotor and generating an electric current.

In a nuclear power plant, nuclear reactions create heat to heat water, which turns into steam, which goes through a turbine, which spins...spinning the rotor and generating an electric current.

In a wind turbine, the wind pushes against the turbine blades, causing the rotor to spin...spinning the rotor and generating an electric current.

In a hydroelectric turbine, flowing (or falling) water pushes against the turbine blades, causing the rotor to spin...spinning the rotor and generating an electric current.

So you see, the different energy sources just provide energy to do the same basic thing...spinning the rotor and generating an electric current.

*The "fine print" on this electricity discussion

The approach described here (which uses electromagnetic induction to generate an alternating current) is just one way of producing electricity. There are also photoelectric, electro-chemical, electro-mechanical, and thermoelectric phenomena (just to name a few) which can be used to produce an electric charge or direct-current electricity. You can generate an electric charge simply by wearing leather-soled shoes and shuffling your feet while walking on carpet (if the weather is dry enough). Batteries are based on chemical reactions - you can make a simple battery by using an orange and two nails of different metals. Photovoltaic cells use light waves of specific wavelengths to excite electrons to cross from one layer of a semiconductor to another. A thermocouple can generate a current if the temperature at each junction is different. Fuel cells use hydrogen.

Nevertheless, most of the electricity that powers your toaster (or your computer, television, refrigerator, etc.) when you plug it into a wall outlet is usually produced using the approach described here.

Links

Boston University Physics II course notes:
buphy.bu.edu/py106/notes/Electricgenerators.html

Encarta Concise Encyclopedia:
encarta.msn.com/encnet/refpages/search.aspx?q=electricity+generator

Exploratorium (science museum in San Francisco):
www.exploratorium.edu/snacks/motor_effect.html

How Things Work (physics of everyday life):
rabi.phys.virginia.edu/HTW/electric_power_generation.html

Federal Energy Regulatory Commission:
Staff report on reactive power. 177 pages. If you REALLY want to get into the details:
http://elibrary.ferc.gov/idmws/File_list.asp?document_id=4273982