Microphones

Microphones are transducers (LINK).  They convert acoustical energy (sound waves) into electrical energy (voltage).

Although the method is slightly different in each type of microphone, every microphone uses a diaphragm - a device similar to the human ear drum in that it moves in response to the changes in air pressure as a sound wave passes through it 

Faraday's Law:

http://www.physics4kids.com/files/elec_faraday.html

Dynamic

In a dynamic microphone, the diaphragm is attached to a coil of wire that surrounds a cylindrical magnet.  As the diaphragm moves in response to the acoustical energy, the wire moves relative to the steady position of the magnet, creating the necessary electrical impulse.

Condenser

In a condenser microphone, two metal plates are positioned parallel to each other, and separated by an air gap.  The first plate is stationary, and receives an electrical charge from a power source (typically a battery, or +48V phantom power).  The second plate is non-stationary, and functions as the diaphragm.  As the diaphragm (the second plate) moves in response to the acoustical energy, the variance in the electrical field *between?* the two plates creates the necessary electrical impulse.

Boundary Microphone

A boundary microphone combines a very small condenser microphone with a boundary plate. Although the microphone component is typically only 1/4", the boundary plate provides a larger surface area representation that reflects sound toward the diaphragm, and is specifically engineered to provide an in-phase representation of sound to prevent phasing problems that would otherwise become problematic with a diaphragm large enough to capture the acoustic energy of the desired surface area.

Other types of mics

Shotgun microphones are incredibly directional.  They will pick up sound from a very narrow (but deep) area in front of the microphone, and ignore essentially all of the sound from either side. Parabolic microphones utilize a reflection technique to concentrate the sound onto the transducer.  Neither of these microphones are incredibly useful for live sound reinforcement because of their characteristics.

Pickup Patterns

Thinking back to the goals of sound reinforcement**, it becomes important to be able to "focus" the source of acoustical energy from which a microphone generates its electrical signal.  In a live stage environment, for example, a microphone that is designed to "listen" to sound coming from all directions might create a feedback issue regardless of its position, where a microphone designed to "listen" from one side can be situated in such a way that eliminates the potential for feedback when positioned with the front away from the speaker.

Pickup patterns are represented by polar graphs.  Although they are 2-D in nature, it is understood that they represent a 3-D space.

Omnidirectional

Omnidirectional microphones will evenly pick up sound coming from all directions.

Typical examples:
Lavalier microphones

Cardioid

Cardioid microphones tend to ignore sound from behind the microphone. Their pattern looks something like a heart, hence the use of "cardio" in the name.

Hypercardioid

Hypercardioid (or supercardioid) have a narrower pickup pattern on the front of the microphone than a cardioid microphone, but will also pick up sound from a (relatively) narrow section of the back of the microphone.

Figure 8

A Figure 8 (or bidirectional) will combine sounds picked up from the front and back of the microphone, and will tend to ignore sound from either side.

Additional Types & More Info

You can find more information about microphone polar patterns on Wikipedia.

Instrument Pickups

A "pickup" (typically for an electric guitar) utilizes one or several magnets to establish a magnetic field and one or several coils of wire that allow for changes in the magnetic field to be converted into an electrical signal.  Conductive metal strings are placed within the magnetic field.  As the strings are plucked, their vibration causes a disturbance to the magnetic field, which creates an electrical current through the inductive coil that then travels through a wire.

Synthesizers & Samplers

Synthesizers and samples generate electrical impulses based on pre-determined patterns.  The electrical impulse from a synthesizer is generated through an oscillator that outputs a cyclical waveform at the frequency corresponding to the desired pitch. The sound is shaped through the use of "envelopes" and "filters" (which are beyond the purview of this reference).  The electrical impulse from a sample is generated through a playback mechanism, where a device will "play back" the electrical representation of a pre-recorded sound file or pre-synthesized waveform that corresponds with a specific pitch. 

Playback Devices

A playback device simply plays back pre-recorded audio.