So Microsoft Canada has had this thing going on for a while now called the Developer Movement (Twitter and via #DevMov, Facebook). Basically, you build some apps, learn some new things, and win prizes. Back in March, they held an extra special, super-duper, amaze-balls (it was pretty great, really) side contest called #DevMania. Get a lot of points and maybe get a phone (Lumia 1520). So I got a phone. And that began the restore process.
The first step is to make sure your current phone is backed up. Go to the settings screen and find backup. Adjust the backup settings to your liking and run it. You want to make sure you get the most recent data.
While that is running, start your new phone. Go through the setup process, but DO NOT associate an account. You need to get all the system updates first. On the new phone, go to settings and find phone update. Check for updates and install them. Repeat this process until there are no more updates.
At this point you should have two phones: one fully updated, one fully backed up. Now, on the new phone, go to settings and find about. In about, tap the reset your phone button. You see, a backup can only be applied to a phone at setup, and only on a phone with a similar version. So, if you old phone is running 8.1, but the new one had 8.0, you can’t apply the backup. The update took care of this, so resetting the phone will only affect personal settings/apps, not system updates.
Now, when you run the setup process on the new phone sign in with the same Microsoft account you used on the old phone. You should be presented with a series of backup options. Choose the one that you created from your old phone. After the initial setup your start screen and settings will be present and your apps will start downloading. For an even more thorough update, run the Transfer my Data app (comes standard on most Windows Phones) on the old phone and follow the instructions to move local contact info to your new device.
And there you have it! A fully transferred Windows Phone, ready to use.
UPDATE: So, back in WP8, there was a bug that prevented pushing backups to the server. I’ve not run in to this since the 8.1 update, so I thought it was fixed. Thanks to Joel for pointing out he still hits it. The fix is to change your background to one of the default images that came with your phone. Thanks again to Joel!