Fourth: When Live Needs to be Louder

A basic PA signal flow goes like this: Microphone, mixing desk, Amp, Speakers.
that's it. a lot of small mixing desks have a simple EQ and effects set up built into them, because carrying around a EQ and Effects rack is not really that feasible when your only working with a small PA set up, then there is the idea that in a small pub there is only so much you can do, its still going to sound like your in a pub. everything else is pretty simple from there with a small gig, though it does depend on what the bands instruments are and all that complicates is your Channel list and microphone selection.

Channel lists are basically just a big list of the instruments that will be used, the channel that they will go into on the desk, the microphone that will be used on that particular instrument and any effects that will be put on it. obviously the bigger the gig the bigger the channel list and the bigger the desk needed, but all gig, big or small, have a channel list.

Microphones are these things that turn acoustic energy into electric energy and they come in different shapes and sizes for different jobs. tricky instruments have special microphones made for them so that they fit in the most acoustically sound place on that instrument. they also have a polar pattern on them which is the direction around the microphone that will pick up the sound, all microphones have a polar patters and all of them fit into one of two categories: Dynamic and Condenser.
dynamic microphones are very robust, they are the tanks and units of the microphone world. they sound wonderful and last a long time, they are wonderful for anything that is very loud, they are not very good at quiet things though. they have a electromagnet inside them that turns the acoustic energy into electric energy.
Condenser's like quiet things and they need to be handled with care as they have a diaphragm inside them that can destroy a microphone if it is popped.

Big gigs are very different because the chances are you have a team of very strong men to help you carry them around. the signal flow for a big gig looks like this:
Microphone, Multicore (a big wire which cases lots of little wires, also called a snake), mixing desk, EQ rack, Effects Rack, Crossover (which splits the signal into High, Mid and Low signals. so it can be split into the right monitor), Amp, Monitor.
There is also the added complication of FOH and monitor engineers.
at a really big gig there will be a separate desk in the middle of the crowd somewhere that just deals with the sound that the audience hears, and then there will be a guy in the back that controls what the band hears on stage. The FOH engineer will send an untouched mix of all of the instruments to the monitor engineer via a multicore. the monitor engineer will then send it to the appropriate places.
this can be done in 2 ways, the band can have monitor wedges on stage or they can have wireless in ear monitoring. usually it is the in ear idea as this leaves more room on the stage for them to perform.

Sometimes with a large PA, such as a festival there will be a flown set of monitors attached to a truss and then there will be another in the crowd, and sometimes the sound doesn't get there in time, the way around this is to delay all of the monitors slightly so that they play the sound at the same time. its a very complicated process that involves a lot of science.