I edited Phil's instructions for applying the update. This is how I did it and it worked. I am on the stock rom with an unlocked bootloader. Hope it helps
The prerequisites:
You need the
Android SDK installed. Note the path.
You need fastboot. (
Windows)
You need to unlock your bootloader. If you haven't done that (and you really should),
here's how.
Download the update
here.
Download the latest ClockWorkmod recovery image from
here.
Now, the instructions:
Copy the OTA package above to the /sdcard folder on your Galaxy Nexus
Drop the ClockworkMod file in the same folder you have fastboot in on your computer in the SDK folder (either /tools or /platform-tools). Rename it to cwm.img to make things easy.
Reboot your Galaxy Nexus to bootloader mode (hold volume-up and volume-down, then press power).
Plug your phone into your computer, and open a command prompt or terminal. Navigate to the folder with fastboot and the cwm.img inside it.
At the command line, type the following: fastboot.exe boot cwm.img
Use the ClockWorkMod recovery menu to flash a zip file from the SD card, and choose the OTA zip file you downloaded earlier.
Let things run their course.