Nexus devices are commonly revered for being among the first devices to get the latest Android software from Google when they announce, and push out a new software build of the latest flavor. This includes the most recent build of software, Android 5.1 Lollipop, although Android One devices reportedly started getting Android 5.1 before most Nexus smartphones and tablets. If you're a Nexus 6 owner, Android 5.1 has likely already started hitting your device if hasn't done so already sometime over the last week. This doesn't however apply to Nexus 6 owners who have an AT&T branded Nexus 6, as well as presumably anyone using an unlocked model that is running the device on the AT&T network.
This doesn't mean that you can't update your Nexus 6 to the latest version of Lollipop prior to when AT&T pushes things out officially. The steps don't take long and the whole process is relatively simple, and it doesn't involve flashing anything so this can be done by non-rooted users which makes this user-friendly and for the most part, quick. As noted by Android Guys, the first and most obvious step is to make sure that you backup your device. Unless there is absolutely nothing on the device you want to save, proceed to the settings menu and navigate to Backup and Restore section, tap to enter that menu, then hit the backup button and select the account you wish to backup important data to.
After the backup has completed, the next step is to take out your SIM card. Use the SIM tool that should have come with the device in the box or something small enough to poke into the hole of the SIM tray and pop it out, remove the SIM, and then navigate back to the settings menu, enter into the Backup and Restore menu again and initiate the factory data reset on the device to restore your phone back to factory settings. There will be an option during this process to restore your device from the most recent backup that was created, and in choosing this option you'll be setting things back to the state of your device before you pulled out the AT&T SIM. After the restore is complete, the phone should reboot and you should end up with a status notification (which may or may not pop up immediately) alerting you to the ability to update to Android 5.1 Lollipop.