HOW ELECTRIC GUITARS WORK
Introduction
If you’re like me, you may have wondered how an electric guitar works. As an alternative rock fan I listen to the instrument often and have always been curious about how the instrument works. Unlike its cousin, the acoustic guitar, it does not work though resonance inside the instrument’s body produced by the strings' oscillations. The most obvious problem: the electric guitar has a solid body.

The question then becomes, how can a solid bodied instrument produce sound through vibration? The answer can be found in the name of the instrument itself. It works through the science of electricity.
A Brief History
Engineers began experimenting with electrical instruments as early as the 1800s. However, the first attempts at an amplified instrument did not come until the 1920s. The first commercially advertised electric guitar was made by the Stromberg-Voisinet company in 1928. The electric guitar as we know it now first hit the music scene in the 1930s. At that time few people saw its potential. However, it has since become the staple of modern rock music and an iconic American instrument.
The Science Behind the Sound
How a Pickup Moves Vibrations:

In order for an electric guitar to produce sound, oscillations of the metal strings are sensed by electric pickups (small, powerful magnets at the base of the strings). “The magnetic pickup of an electric guitar uses electromagnetic induction to convert the motion of a ferromagnetic guitar string to an electrical signal.” (Horton, Moore). In other words, the pickups send electromagnetic signals to the amplifier, or “amp”, and the speakers.
The pickups themselves, although small, are some of the most amazing pieces of the electric guitar. Their name is quite fitting. They “pick up” the vibrations created by the guitar’s metal strings and help carry them to the amplifier which produces the sound we recognize as that of the electric guitar.
A pickup is made up of a bar magnet wrapped with as much as 7,000 turns of wire that is often as fine as human hair. When this magnet picks up the vibrations from the metal strings it transfers them through the wires connecting the pickups to the amplifier where the sound is transformed and amplified.
Disected! How This All Works:
If you have ever heard an electric guitar played without an amp you have heard the difference the amp makes in its sound. The amp is so crucial to the guitar’s sound that without it we hear a completely different sound, not the smooth vibrations we are used to. Instead, the guitar produces a smaller ting-y sound.
Electric Guitar Being Played Without Amp:
Guitar Played With an Amp:
There is no need for me to post a video of this. All you have to do is turn on your iPod or a local radio station. Modern music is full of the sounds of the amplified electric guitar!
My Sources
N. G. Horton and T. R. Moore, Modeling the Magnetic Pickup of an Electric Guitar, American Journal of Physics, Feb 2009, Vol 77, Issue 2, pgs. 144-150.
Very in-depth and technical article about the physics involved in the pickups. I wouldn't recommend reading the entire article unless you are a physics major.
However, the "introduction" section delves a little deeper into the topic than I could have done in this page. A highly credible peer-reviewed source.
How Stuff Works: How Electric Guitars Work, Marshall Brain, Published by Discovery, http://entertainment.howstuffworks.com/electric-guitar.htm
Very simple, informative article all about how electric guitars work and some history of the instrument. Includes diagrams and video.
Possibly the most useful site I looked at. Very simple, but detailed descriptions.
Very credible sponsoring company and author bio shows good credentials.
Youtube:How An Electric Guitar Works, Discovery Channel, http://www.youtube.com/watch?v=lBAZepM5F_0&feature=channel_video_title
Really great summary of how the guitar works and it is really cool to see them take it apart! Very useful for quick, informative overview of the topic with lots of neat facts.
Although the uploader was not a very official person, the video came from a national television network known for scientific programming.
Where I found my images: