How do you wire cooling fans for an E46 LS swap?

The same way as any swap: relays for the fans, and a temperature signal to trigger them.

• Two fans → two relays. One standard relay for both fans can blow its ~30 A fuse when they start together.
• Trigger: a thermostatic switch, a gauge or controller with a fan output, or your ECU's fan output (most aftermarket EFI has one).
• Power: fused constant power to the relay feeds, switched ignition power to the relay coils.
• Options: run the second fan off the A/C compressor signal or a manual switch for extra cooling.

We don't have an E46-specific fan source, so check the fan's current draw against your fuse and wire sizes.