Best practices for updating a theme

My blog’s theme has had updates available a dozen times so far and each time I click to update the theme automatically it does so without incident. Hooray.

But what if one of these days something went wrong? Could something going wrong wile updating a theme cause the blog to “crap out”? If so, what is the best practice for being safe?

I assume you’re about to say “back up your currently installed theme first” but what exactly does that mean? Is that something I do with FTP? Do I switch to an alternate theme first and then rename the theme I was already using? What exactly is the correct process for safely upgrading your theme?