Microphones

Decent mics are really important, always for good sound, but also for sheer robustness to stand-up to live band use.

Two categories of common mic; Dynamic and Capacitor. Dynamic are most common in live situations as they're more durable and cheaper.

DYNAMIC

Low impedance, balanced microphones. They need no electrical power to operate and work much like a 'speaker' cone in reverse. A diaphragm collects the movement of the air (ie: sound) and passes the movement to the coil, wrapped around a magnetic 'north' pole with 'south' as surround. This is essentially the CAPSULE.
Assembly of diaphram and coil is heavy, so has inertial problems. Commonly, no more than 16kHz can be collected (as can't accelerate/decelerate quick enough). The Electrical signal is very small, but most live work has very loud sound sources close to mic (and small signal runs). 
This is the main disadvantage of Dynamic mics; LARGE amounts of gain are needed to boost the weak signal, so signal to noise ratio is low. However, they can handle very high volumes well, so they are the only mics used to collect guitar amplifiers.
Dynamic mics using Neodymium as a magnetic material can have smaller coils, so claim to respond to up to 20kHz.

CAPACITOR (or Condenser) microphones

These are far more sensitive than dynamic mics so are better for quiet or distant sources.
They have a diaphragm, but no coil assembly, so they have a better response than dynamic mics as the assembly is much lighter.
A metalised diaphragm moves in front of a fixed metal plate (drilled to allow passage of air). 
A fixed electrical charge is applied to the two surfaces; as the distance between them changes, the voltage also changes.
An amplifier integral to microphone amplifies signal giving a strong output level. 
This is why capacitor mics need "Phantom Power".
The diaphragm and back plate form the two plates of a charged capacitor, the PD will change as the distance between them changes, by monitoring this voltage across a power-resistor using a high-impedance (FET) pre-amp you create the signal. The metalised coating on the diaphragm can be made very thin, giving excellent response.
The simple capacitor mic is, however, far from symmetrical when in use. acoustically the diaphragm flexes (like a drum skin) and electrically there is an electrostatic attraction between the metalised skin and the rest of the capsule. This problem can be overcome by building the capsule with (drilled) plates both behind and in front of the diaphragm. This also greatly reduces intermodulation distortion and is how virtually all cap mics are made.
Usually, capacitor mics are far more expensive than dynamic and also less robust. As such, capacitor microphones are rarely found in live 'band' situations.
Capacitor mics can suffer from condensation build-up from the singer's breath, which basically connects the diaphragm and plate, spoiling the delicate resistance. Can be significantly reduced by using a pop-shield.

RF CAPACITOR Mics 

Rare system, today mostly used and perfected by Sennheiser. Rather than using a fixed charge across the 'plates', a RF AC voltage is applied and the 'audio' is superimposed on the RF oscillation. This has an inherently high impedance, so moisture has little effect. Circuitry extracts the signal and outputs as 'normal'.

ELECTRET Mics 

A capacitor mic where diaphragm has permanent electrical (magnetic) charge sealed into it, eliminating the need to charge it. A pre-amp still needed, but can be battery (not just phantom) powered. Originally they were shite, because the magnetically charged diaphragm was thick and heavy, giving little benefit over dynamic mics, but now the process is refined and the response is more desirable, especially with Back-electret technology.

BACK ELECTRET Mics

Here, the permanent charge is sealed into the back-plate; so the diaphragm can be the same as is used in conventional, great-sounding Capacitor mics (a thinly metalised film). Can ultimately offer same performance as conventional capacitor mics at a far lower cost.

VALVE Mics

Bastard expensive, very fragile, need own dedicated high-current power supply. Very very rare in live situations as they break easily.

RIBBON Mics

Working like a dynamic mic, a 'ribbon' of aluminum performs the job of diaphragm and coil. Here, the ribbon acts as a coil with only a single turn, so signals are very low from the 'capsule' and require transformer to amplify the signal. The light weight of the ribbon gives excellent frequency response and is mostly used in classical string recordings due to their unique sensitivity and subtly.

DIAPHRAGM SIZE

Although a larger diaphragm, obviously will collect more raw 'signal' and give a higher-quality sound, and is therefore desirable, it can present problems when the original sound is arriving at an angle. Parts of the original wavefront will become out-of-phase, especially HF. Again, the larger diaphragm will have greater mass and limited freq. response. Larger diaphragms mean a larger overall microphone size, and this may interfere with the field of sound trying to be recorded. The larger size tends to lend itself to accurately recording bass frequencies (like larger drivers reproduce bass better) so most commonly found in kick-drum mics.

PHASING

Mics should translate an increase in air pressure into an increase in voltage, then translated to a +ve movement in the cone of a loudspeaker. Wiring problems can set any signal out-of phase, either by reversing the poles (on unbalenced signals) or by "swapping" pins 2 and 3 on a balanced lead. Problems will then become evident when combining in and out-of-phase signals, as they will cancel (quite obviously).

PHANTOM POWERING

48v DC, where present is delivered down the signal pins of balanced-line systems. The signal is then resolved using +48v as a "ground" level. Both of the signal lines have +48v present on them, with ground used as 0v. This allows any balanced, non-powered equipment to "see" the same voltage across the voice coil and thus not be damaged. HOWEVER, there is a significant chance that, during connection, one pin of the connector will close slightly before the second, allowing a voltage imbalance and damaging the microphone. SO, it's advisable, where possible to turn-off phantom power, or to only "power up" when all connections have been made.

IMPEDANCE

High and Low. High impedance (5-10kOhms) found in budget home equipment, as output voltage is relatively high, allowing use of far cheaper circuitry in the preamps as the gain can be far less. High impedance is FAR more susceptible to induced interference, AND, the higher the impedance, the more important cable capacitance becomes.
Capacitance attenuates higher-frequencies, so high-impedance mics can only have cable runs of max. about 7m, plus handling noise, where the movement of the cable varies the capacitance characteristics, producing noise.
Low impedance - Generally below 250 Ohms, with pre-amp of around 7-10 times that figure, as maximum voltage, not power transfer is desired. Differing the impedances also reduces the effect of cable capacitance still further, allowing runs in excess of 50m with little capacitance-based loss.
Cable resistance has a negligible effect for both high and low impedance microphones.

DIVERSITY RADIO MICS

Two receivers, the signal from the strongest is used. Two antenna are used.
Because reflections from walls etc. can cause radio 'dead' spots, a problem with single receiver systems, diversity systems have two antenna, sufficiently far apart for one to always have a signal, even if the other is in a deadspot.
Squelch - A simple gate, squelch controls a mute threshold, of minimum 'signal' strength to allow receiver to output a signal.

POLAR (or pickup) PATTERNS

Omnidirectional

All directions, surprisingly... The diaphragm is fixed across the end of a sealed, airtight chamber. This means that one side of the diaphragm is at a constant pressure, so the diaphragm moves in response to changes in air pressure, virtually regardless of the direction it arrived at. Also called a pressure microphone. They do not have 'proximity' effects inherent in cardioid and figure-eight mics. Generally sound more natural as there are is no 'porting' found on directional mics.

Unidirectional (Cardioid)

One direction, often called CARDIOID because it's polar pattern is roughly heart-shaped.
Good for artists that move around slightly, but watch out for pickup from on-stage backline. Virtually no pickup from behind, so put monitor speakers directly behind mic. Built like a figure-eight microphone, but uses a 'sound path' to direct sound into the rear of the diaphragm. This network of refectors is complex but has the effect of canceling sound from the sides and rear of the microphone, leaving it sensitive to the front.

Hyper and Super-Cardioid

Narrower cardioid pattern so more directional, but picks-up more from directly behind; frequency response also often narrower. (Why I don't like Beta 87's very much, they sound funny and pick-up monitors more). Monitors must be slightly to the sides for these.
Shotgun mics have an extended 'tube' of soundpath, making them very directional, but dispersing much LF noise.
All cardioids types work by sensing pressure gradient (difference) between the front of the diaphragm and the 'ports' (holes) on the rear of the capsule that feed the interference network. Dynamic characteristics can be fucked-up if the mic is held too close to the basket (grilly, 'head' shaped bit); also this significantly increases chances of feedback.
Dynamic and Back-electret both have fixed polar patterns, but in studios you can find dual-diaphragm capsule capacitor mics, where pickup can be changed by a switch, which changes properties of the capsules.

Figure-of-Eight

Uses diaphragm open to the air on two sides, SO it picks up from the front and back of the capsule, but not the sides. Uses the pressure difference between front and back to work, also called pressure-gradient mics. Proximity effects are simply an increased low-end response when very close to the source. 
Used to be used on the chunky old chrome 50s mics, but now reserved for specialist stereo applications. 

PROXIMITY EFFECTS

because the mics directionality is based on the relationship between the front and the ports at the back, if the source (ie singer) is closer than about 5cm, you get significant bass boost, as the acoustic path differences between sides of the diaphragm within the mic become significant and phases begin to change in the LF reigon. Standup comics commonly demonstrate this. 
Can be used by skilled singers to add tone to their performance but can equally sound really rubbish with an inexperienced singers.

SENSITIVITY

The sensitivity of a mic, given in dB, is the electrical output for a given SPL, usually 1Pascal (94dB @1KHz). A good level is abour 8mv/pa.

NOISE

The level of external sound needed, on a perfectly noise free microphone, to produce an output equivalent to the output of the mic in silent surroundings. "Flat" response uses 20Hz-20kHz signal, as opposed to "A-Weighted Response", which uses frequencies similar to the response of the human ear (generally about 2dB less).
DYNAMIC RANGE - Obtained by subtracting the base-noise level from the maximum SPL the mic can handle without distortion. Often very high (~115dB), but remember this relies on sound approaching the max. SPL, SO, quite often, a more sensitive microphone with lower range will be far better at recording a quieter sound.

HANDLING NOISE

From the obvious design differences (eg: 57's rattle) to the less obvious like cheap, creaking cable. Main noise arises from mic technique. When stand-mounted, rumble (like footsteps or physical feedback) can be transmitted from the floor and up the stand (use 100Hz filter on the desk).

SIGNAL NOISE

Any electrical circuit that presents a resistance can create noise, due to quantum effects of the electrons within it. On this principle, the higher the resistance, the more 'random' noise generated but the combined circuit. Similarly, random impact of air molecules on the diaphragm can also contribute, albeit a tiny amount.

POP SHIELDs or 'spit screens'

Small fabric screen used in studios to eliminate 'wind' pops from vocalist (in 'P' and 'B' sounds). Foam has little effect, so for live use, mic technique must be used to avoid popping.

COMB FILTERING

Where using a "standard" mic quite far away from the source, signals reflected off walls / objects become significant and start to cancel the desired sound at the capsule. Results in a sound similar to Flanging and it really sucks (very nasal).

BOUNDARY MICROPHONES

Or PZMs (Pressure Zone Microphone). Designed specifically to work against a wall or floor (ie: boundary) and collect sound arriving at that point, regardless of direction, but WITHOUT the comb-effects that would be found with a 'conventional' mic in a similar situation.
It relies on the principle that against the wall, the air cannot actually move, because it's mass is tiny compared to the mass of the wall (obviously). Where this happens, reflected sound (instantaneously) becomes a change in pressure, rather than wave-vibration-transmission. Placing a sealed, pressure-based mic capsule at this exact point will accurately reproduce the sound. The capsule can either be recessed into the plate, or suspended just above the plate. As the direction of sound is unimportant (just pressure at the point)  the capsule blocks surprisingly little sound from reaching the diaphragm. As long as the capsule is not more than about 2.5mm from the plate, original and reflected sound will remain in-phase up to around 20kHz. Because direct and reflected sound arrives in phase, the mic has an instant 6dB of "noiseless" gain over other techniques.
PZMs are often supplied with a metal backing 'plate' to replace the wall or floor, allowing them to be position more usefully. But, the size of the plate will effect LF response. Assuming a square plate, a 6dB drop-off can be expected at freq. with wavelengths six times larger than the length of one side of the plate.
The polar pattern of almost all PZMs is a hemisphere, created against the boundary.
PZMs are very useful for capturing discussions around a table, or anywhere where refections off a surface close to the source pose a problem.