This is the exact method I used, courtesy of TGA_Gunman on XDA Developers, who in turn thanked a bunch of other people.
First, you need to download three things:
1) The Nvidia NvFlasher program:
Multiupload.com - upload your files to multiple file hosting sites!
2) The Nvidia NVFlash APX drivers:
3) The flashable root file
Install the APX drivers, then follow these instructions:
1. Remove the battery.
2. Plug the USB cable into your PC.
3. Hold Volume Up and Volume Down at the same time keeping them held down.
4. Plug the USB cable into your phone. (Keep the volume buttons held until Windows detects a new APX device.)
5. Open Device Manager in Windows and you should see "APX Device" listed with an error icon.
6. Right click on the APX device.
7. Select 'Update driver software'.
8. Select 'Browse my computer...'.
9. Select 'Let me pick...'.
10. Select 'Have disk'.
11. Browse to directory you extracted the driver software to: One-Click-G2x-recovery-flasher-09-04\APX.
12. Accept any warnings, including the big red alert (you may need to disable UAC).
13. Now in Device Manager under 'USB Controllers' you should have an 'NVIDIA USB Boot-recovery driver for mobile devices'.
If not, uninstall the driver, reboot, rinse and repeat.
14. When the drivers are properly installed, unplug your phone.
Now follow these instructions to flash ClockWork Recovery:
1. Remove the battery.
2. Goto the NvFlash directory and Double Click "OneClickRecoveryFlasher.exe".
3. Make sure the USB cable is unplugged from your phone.
4. Hold Volume Up and Volume Down at the same time, and keep them held down. (Keep them held until you see the "S/W Upgrade" screen on your phone after you complete step7!).
5. Plug the USB cable into your phone.
6. Click the "Flash ClockworkMod" button.
7. You should see it send a bunch of files to the device and the phone screen should say "S/W Upgrade - Please wait while upgrading...". Once the files are sent and the program is finished running in the command window, you can just unplug the USB cord, even while it still says "S/W Upgrade - Please wait while upgrading...".
8. Put the battery back in.
Once the phone has ClockWork Mod flashed, plug it into your computer and copy the flashable .zip file to your SD card.
Turn your phone off, and press the volume down and power buttons at the same time. When the LG logo changes to one with some blue streaks behind it, let go of both buttons and the phone will boot into ClockWord Mod.
Use the volume buttons to move around in the menus and the power button to select in ClockWork Mod.
Select "wipe data/factory reset"
Select "wipe cache partition"
Select "install zip from sdcard"
Select "choose zip from sdcard"
When it's done, go back in the menus until you get to "reboot system now" and select it.
Once your phone has rebooted, it will be permanently rooted!
Once again, I can take no credit for any of this! I've just collected the information and links from XDA developers and consolidated it all here.