Ground means whatever is attached to this symbol in the schematic:
Everything that touches this symbol in the schematic is actually connected to everything else that touches the symbol. Since so many things connect to it, this makes the schematic easier to read.
Usually the negative side of a battery is attached to that. But, there are many circuits that work differently. Some circuits need a negative voltage, so the positive side of a battery would be "ground". Some circuits need positive and negative voltages, in which case there could be two batteries, one with the negative side attached to ground, and the other with the positive side attached to ground.
This works because voltages are relative. Put three \$10k\Omega\$ resistors in series, and attach them to a battery. The difference in voltage from one side of the battery is 3V (because it's a 3V battery). The difference in voltage from one side of a resistor (any of the three) to the other side of the same resistor is 1V, because the battery's 3V is divided among 3 resistors of equal value.
Since voltages are relative, ground exists as a sort of assumed reference voltage. If we say an input is "5 volts", we mean "the difference between the input and ground is five volts".
In the context of AC, things aren't really different, except that tradition has done a good job of making the same term "ground" mean many things. It still could mean whatever is attached to that symbol, or it could mean that 3rd connector on the wall. More on that later.
As far as the circuit is concerned, live and neutral are no different. Pick either one, and the other oscillates between a higher and lower voltage, relatively. If all you have are those two wires for reference, they are indistinguishable.
The difference is more important when you consider safety. The things around you are at some particular electromotive potential (voltage). Current flows when there is a difference in potential. The neutral AC line should be about the same potential as most of the things around you, so in theory, if you touch it, and also Earth, you don't get shocked, because there is no difference in voltage. If you touch the live wire, you do get shocked, because there's a difference in potential.
However, I said neutral should be about the same potential as Earth, and since you are probably touching Earth, you. But, I wouldn't trust your life on it. There could be a faulty transformer on the pole near your house. There could be a lightning strike nearby. The house would be wired backwards. Or, as I mentioned the circuit will function even if the wires are reversed, it could be plugged in backwards. In the US, one of the prongs is a bit fatter to prevent this, but you never know. This is why there's the third connector, called ground or earth. This should go to a big copper rod near your house stuck in Earth, like this:
It doesn't otherwise connect to anything else. There are some times this is important for safety, and other times it's important for other reasons. Point is, it has nothing to do with the electrical power supplied to your home.
How can I tell if I need to ground something to earth vs. "ground" to the negative terminal? When do I ground to the chassis of my device?
If we are talking about a device that plugs into the wall, leave these questions to someone else. Each country has safety regulations, and these regulations exist for good reason. Buy a DC power supply that takes care of all that for you, and connect to its output, and nothing else. Don't connect to Earth through the 3rd pin on the wall or you may circumvent the safety features of your power supply.
If you are wondering if the "ground" symbol on your schematic should also be connected to box your project is in, well, it depends. Maybe you want to do that for RF shielding. Or maybe you don't, because you don't want some other device with a different idea of "ground" to touch it, which could result in noise in your circuit or melting something. In many circuits, it doesn't matter at all.
(1) Does 'input 2' correspond to the +12V wire and 'input 1' to the -12V wire?
NO. This is connected to the power supply connector. (Pin 1 is the positive, pin 2 the ground or 0V). The INPUT connector is where the audio signal goes (2) is the live and (1) is the ground.
(2) When I see the symbol 'ground' on the schematic does that mean that I need to connect those to the -12V line? I have no 0 volt line in the circuit so what is the ground line?
All voltages are relative to each other. If you only have TWO wires from the AC/DC converter then the most positive is taken as the positive and the other one is the OV or ground. A simple check with a voltmeter will determine which is which.
(3) Why are C3, C5 non-polarized capacitors and why are the other ones polarized? The current flows from negative to positive. Does that mean that the polarized capacitors need to be placed with their positive legs pointing to the left?
C3 and C5 are small value capacitors (0.1uF). These can be easily made as physically small, non-electrolytic types. They have the advantage of being able to decouple (short out) the higher frequencies. The larger values (uFs) are made as electrolytics as these can be made with high values in small physical packages. They are generally much poorer at handling the high frequencies. By combining an electrolytic with a non-electrolytic capacitor in parallel (eg C3, C6) you get a much better response over a wider range of frequencies. In this case they are used for 'smoothing' the supply voltage, preventing hum and hiss. The positive plate of an electrolytic is shown as an open rectangle but left and right (or up, down) have no meaning in terms of connection as this will be determined by board layout. Conventionally current is taken to flow positive to negative.
Best Answer
Strictly speaking, they aren't required, but those resistors help speed up the turn-off of the associated transistors, and also help with noise immunity by pulling the base connections all the way to ground when the switches are open.