How do I connect the wires on a PC Power Supply that supplies +3.3V, +5V, +12V, -12V, and +5Vsb to make 15 Volts for Peltier module?
You can't directly. 

In order to get 15V from a PC power supply at any significant current, you would need a step up (boost) converter - a switching regulator to generate 15V from the 12V rail.

For very low current (~500mA), you can use the +/-12V rails to get 24V and then regulate it down, but you couldn't use that for your application because you would overload the -12V rail.

Alternatively (and probably most sensibly) buy a 15V PSU to begin with. Not much point going from 110/230V to 12V just to go back up to 15V.