The ordinart AT PSU you find in older PC's have 2 flat connectors, with 6 pins in each, that powers the motherboard. One of these connecotr have an orange (Power Good) and a yellow whire (+12V) and you need to connect these two whires together in order to get the PSU to work.
Then you should find some power connectors on the PSU that goes to harddrives and diskdrives (you should have 2 power connectors for diskdrives, though there are quite a few PSU with just one). Connect one of them to the diskdrive so it have power, then connect the other to the motherboard so it get more power. Then power up both the AT PSU and the original PSU at the same time.