You can hook the ps-on wire "usually green" to ground "black" This will turn on the power supply. Then use the yellow wires for 12V, red for 5V, and orange for 3.3V. Check your power supply, most have a color code or a pinout. You should keep a small load on the power supply, I find the internal fan is usually enough. or add a resistor to the 5V. If you cut off the atx connector, make sure you tie all the same color wires together. Most power supplies have a sense wire on the 3.3V and 5V that will shut off if disconnected.
Have fun