Just watch out for the different colour codes used.
On most Atari machines the blue wire is the +12V supply.
With most ATX power supplies the +12V supply uses yellow wires.
So connect as follows:-
ATX PSU --> Atari
Yellow -----> Blue (+12V)
Red --------> Red ( +5V)
Black ------> Black ( 0V Ground)
Green --------------> connect to one of the ATX PSU black wires (switches the PSU on)
simbo's answer to a similar question - viewtopic.php?f=15&t=19289#p167253
modtown - article - Powering an ATX PSU Without a Motherboard - http://modtown.co.uk/mt/article2.php?id=psumod
GideonTech_com Case Modification - Power Up an ATX PSU without a Motherboard - http://www.gideontech.com/content/articles/196/1
PC Power Supply Failure Diagnostics - Computer ATX Power Supply Troubleshooting and Repair - http://www.fonerbooks.com/power.htm
How to Make an ATX Power Supply Work Without a Motherboard eHow_com - http://www.ehow.com/how_4928308_make-po ... board.html
How to Convert a Computer ATX Power Supply to a Lab Power eHow_com - http://www.ehow.com/how_2189437_convert ... upply.html
How to power up ATX PSU without MB - http://www.tomshardware.co.uk/forum/179079-10-power
Using a Second Power Suppy-Adding a ATX Power Supply PSU (plus lots of info) - http://www.directron.com/2powersupplies.html
Guide to Computer Power Supplies (plus lots of info) - http://www.smps.us/computer-power-supply.html
PC Power Supply Connectors and Pinouts - http://www.smpspowersupply.com/connectors-pinouts.html
Of course if you have a multimeter you can test the supply wires before you make the final connections.
Remember that the supply line (wire) that has the highest current rating is the one that the PSU regulates (maintains within a close voltage range, normally 5% or less). Often some or all of the other supply lines (wires) are unregulated (like the +12V and the -12V). So until the PSU is supplying a load (like a computer) the other supply lines (wires) may be slightly lower or higher than you expect.
Falcon, Atari 520STFM, Atari 1040STE, more PC's than I care to count and an assortment of 8 bit micros (nearly forgot the Psion's)