in terms of basic DC power supplies using +12V as VCC or your positive lead, and using -12V as your VEE or negative lead, that will give you 24 volts at your load... or whatever voltage depending on the combination of 5 ,12, and 3.3 you use for + and -. Use the +12 volt as positive and +5 volt as negative, that's 7 volts to your load.
However, on an ATX power supply check the current ratings or DC output specs of the different voltage rails, that's what will either make or break what you are doing.
Generally for an ATX PSU the +12v rail has a high amperage rating like 100+ amps to support high end graphics cards, much higher than any of the others rails. the -12v rail may be rated to do less than 1 amp, so for whatever two voltage rails you use to get a desired DC voltage, the minimum current rating from those two is what you have to stay under or blow the PSU.
only if you use the GND wire and 1 rail will the current rating of just that 1 rail apply.
and also check if the PSU has one 12v rail or multiple. If multiple, make sure you know which rail you are using and what it's current rating is if teh multiple 12v rails are different.
at this point if doing the above you use the PSU gnd as system ground on the device (i.e.) load that is fine, that's how every pc motherboard currently works, that DC ground is connected to PC chassis via mothererboard just like the AC earth ground is to the PSU shell connected to the pc chassis... that you handle while powered.