I hope you're well. This is day 4 of iPad Mini ownership for me. In the time I've owned mine, I haven't actually run a complete backup. Wondered whether it's safe to do so whilst the device is charging.
You can use iCloud to back it up - in that case it will back up automatically when it's charging, online and locked (the screen is black, but it's turned on). In Settings - iCloud - Storage & Backup enable iCloud Backup.
You can backup using iTunes. You connect your device to a computer, and choose File - Devices - Backup in iTunes. In that case it's not always possible to charge it, because you use the USB cable for the computer, and most of them don't provide enough power to charge it.
Update - backed up successfully, installed iOS 7.1.2, still charging. The learning curve's not quite as steep as I thought. Post update restart did scare me a little, though!
I use iCloud. As J. A. says, it is automatic when charging. That way I don't forget to back up. Just like skimonkey, I sometimes use it whilst charging. You will find it is such a flexible device and you will always find any help you need on this forum.
Enjoy your iPad experience and good luck.
Mike