Starting today, and over-the-air (OTA) update is hitting the Sprint variant of the Samsung Galaxy Note 3, carrying the latest Android version (4.4.2 KitKat) as well as some other upgrades to Samsung's proprietary apps, like new launcher settings and a lock screen camera shortcut.
If you haven't received a notification alerting you to the update, you can manually check for it in Setting -> About device -> System Update -> Update.
Now just sit back and let your device do its thing. You'll need to be connected to Wi-Fi, as the update is a little over a half gig in size. And of course, during the update itself, your phone will be a very expensive paperweight. Once completed, you'll be on the latest and greatest from Google and Samsung.
Like the Sprint update, you can manually check for it if you haven't received a notification, or you can download and install the update via Samsung Kies.