Phone applications which are just front-ends for a web service (like Facebook) do not store significant data on your phone and so when you change devices, all you have to do is sign in to the app on your new device and you're done. However apps that store data on your phone like Angry Birds, or our apps Pink Pad and Baby Bump, require a little more TLC.
For Pink Pad and BabyBump, before changing devices, you can go to Settings -> Backups -> Device Backups and back up your data to your phone's internal storage or SD card. If your phone's storage uses a removable SD card, then you can move it to your new device and restore it using the same section of the app.
If you are having a problem restoring an SD Card Backup, check out this FAQ:
If you are using Pink Pad and do not have an SD card in one of your devices, our developers are working on alternate backup solutions.