I just spend the last two days absorbing everything youtube had to offer on this subject.
1) Check the fuse
2) Check for power at the input to the resistor
If those two are good, change the resistor
Other things I'd check to make sure:
1) Is your front controller set to "off"?
2) Check you have power on across the white connector behind the emergency brake panel (orange wire)
I'm not sure, but one of these two fixed my fan not coming on.
After that, I found that I was only blowing hot air. When I checked the hot/cold actuator, I found it wasn't moving correctly. The previous owner had replaced this already. After much more internet searching, I decided to disconnect the ground on the battery for a minute (2001 Tahoe. 2003 and up you can simply remove the controller fuse for a minute). I reconnected the battery and turned the ignition to the on position without staring (two positions). I went in back and watched both the up/down and hot/cold actuators calibrate and home. I waited a few more minutes and started the vehicle. The hot/cold actuator now works and I get cool air. I'll have to wait for the day to heat up a bit and see how well the AC actually works, but at least now I know I'm blowing across the AC coil.