how do i put my backed up info on my new phone?
I got a new iPhone. None of my messages, calendar data or really anything moved over. Do I need to do this manually?
No, you restore the new phone from the latest backup of the old phone. That will restore all of your content. If this was an iCloud backup, it could take a bit of time to restore all content, depending on the amount of content that you had, and that you have a solid wi-fi connection and the device is connected to power. It can take time, and if you interrupt it, it will take much longer.