Updating from iOS 6 to iOS 7 on the Apple iPad mini is as easy as opening the settings, tapping on Software Update, then pressing Install now and agreeing to the Terms and Conditions.
What you need for this update is TIME. At least 20 minutes for the install of iOS 7 from iOS 6 on a iPad without much installed apps. If you have lots of installed applications, it make take more time.
Usually done automatically, unless you disabled this feature or don't have Internet access.
If you skipped this part, you can always select it from Software Update in the Settings application.
Accept the Terms and Conditions.
Usually it takes around 17-19 minutes.
Enjoy your new iPad, iPhone, iPad Mini, or iPod touch with iOS 7.