How do I wire dual electric fans so the LS PCM controls them with low and high speed operation in a third-gen LS swap?

Here is what the documentation says. Each point links to its source; details depend on your exact computer, harness and transmission.

• Holley Terminator X; GM LS: Holley Terminator X fan outputs are Fan 1 on ECU pin B12 (connector E, gray/yellow) and Fan 2 on ECU pin B11 (connector F, gray/red); these are ground outputs that trigger fan relays and must never be connected directly to the fan motor. (Holley (via CARiD mirror))
• P01/P59; Gen III LS; 1999-2007: PSI standalone harnesses provide a dark-green Fan 1 Ground wire and a dark-blue Fan 2 Ground wire at the PCM connector; each grounds the ground side of the customer's own fan relay. (PSI Conversion / Performance Systems Integration (via SlideShare))
• LSx/Vortec: Current Performance's heavy-duty dual-fan add-on module uses three sealed relays and two fuses to run two fans in series at half speed first, then full speed; it has 50-amp relays, one 40-amp JCase fuse per fan, 12 AWG fan outputs, an 8 AWG main feed, and ground-triggered control wires meant to interface with PCM fan outputs. (Current Performance Wiring)

Confirm against the instructions for your exact parts before wiring. More: Other wiring in our tuning guide.