Amplifying a minuscule signal without external power source?
The size of the input capacitor depends on the load following it.  In this case, that's the 39kohm resistor.  The capacitor and the resistor together form a high pass filter.  It's mostly there to keep DC out of the amplifier - it would mess with the gate bias on the FET.  In this case, the cutoff frequency is around 200 Hz. It is not a steep (sharp) filter - the lower frequencies will still get through, they'll be attenuated (weakened) just a little bit.  DC is blocked entirely.  Look up &quot;RC high pass filter&quot; for information on calculating the values.
Each of the resistors and capacitors has a job - they are not magic numbers.  I can't tell you how to calculate some of them, while I understand some of the others.  Take that 10pF capacitor.  It is there to get rid of radio frequency signals - you don't want your cellphone signal blasting through your guitar amplifier.  The 10pF works to together with the 39k resistor to form a low pass filter. It is intended to filter out frequencies above about 400kHz.  The 1.2k and the 4.7k resistors work together to bias the FET into a place where it operate linearly - I know what they are for, but I can't tell you how to calculate them. I'm not sure what the 470pF is doing - probably has more to do with filtering out RF.
The power comes from the connector that goes to the PC or cellphone.  PCs and cellphones expect you to connect an electret microphone to them.  Typical electret microphones have a tiny amplifier inside them, and so need a little bit of DC to operate.  The microphone input accepts AC, but puts out DC for the electret microphone.  This circuit mimics the behavior of a normal electret microphone - it takes in DC (from the phone or PC) and gives out AC (back to the phone or PC.)