If you copy your library first, though, simply follow these steps to add that folder as the library. It's handy to make sure you've done this first if you're copying an existing library as it will create the necessary destination on the drive for you to dump all the files in. Just pick the time and frequency to back up important files from your system onto your My Passport drive. You can set it to run automatically to your schedule.
The key is to tell Steam where it needs to store your games, so it can install them in the right place and knows where to find them when you want to play. This process is important whether you're copying an existing Steam library to an external drive or setting up a brand-new one from scratch to download all your games.
