First things first, please make sure you have “Preview for developers app” still installed and you are signed in and have enabled it for receiving updates. If not, you may not get any “update available” prompt when checking for update.
Now go to Settings—>Phone update—> check for updates. Once prompted let it download the update. 8.10.12397.895 and the whole installation experience takes 15-20 minutes including data restore post update. Once the update is done you will be informed. Check the above screenshots.
As per Microsoft, this update enables some newly commercialized devices and tweaks a couple of new APIs, so you won’t see a difference on your device,
In case you want to read more about Windows Phone 8.1 features, tips, tricks, hands-on, get them all on one page.