I am a complete noob as well! It was easy enough after some reading.
The way I did it was by using this guide:
Guide to Update Samsung Galaxy Nexus (YAKJUXW) to Android 4.0.4 and Get future Updates from Google
I made sure to read everything and follow the steps closely. This method uses Wug's galaxy nexus toolkit (which is designed to help noobs like us).
You don't have to root your phone, but you will have to unlock it, which requires a data wipe (there's instructions for backing up your apps + app data, plus you should manually backup your media to computer) but the short term inconvience of arranging your home screens and reloading stuff again is well worth the long term benefit of direct updates from google in my opinion!