The Android 4.1.2 Jelly Bean OTA update is now making its way to "takju" Galaxy Nexus phones -- meaning those purchased from Google Play or flashed with the takju firmware. It's the same firmware available via factory images, and the one we saw rolling out to "yakju" -- non-Google Play Store -- phones the other day.
Manually updating is the same process as for the Nexus 7 or previous Galaxy Nexus updates. You'll need the file direct from Google (grab it here), adb or fastboot up and running on your computer, and a bit of technical know-how. Rather than re-hash that again here, I'm going to direct everyone to the Galaxy Nexus forums, where this sort of thing is old hat to the hackers-in-residence.
As far as changes to the OS, there are few. We assume that changes under the hood made it worthwhile for Google to send out the update, and we've had no complaints. This is the fun part of having a Nexus phone!