Backing up your style is a good practice to do prior to upgrades or even other large changes to your site/style.
Step 1.) Export your styles
Navigation to the XenForo Admin Panel -> Appearance -> Styles. You'll need to export all of your styles: XenBase, Purchased Style and your child style. The export link can be found here:
Step 2.) Download your style folders
While these don't change often it's also good practice to keep a backup of your style folders. This will be your xenbase folder and your purchased style folder found in your /styles/ folder.
That's it! Your styles are now safely backed up off your forum. To re-install them you'll install them in the same order as if it's a brand new installation.