If you have windows, you can easily plug in both drives and open up a file explorer window for each drive. Size the two windows so you can see both of them. Then tag everything you want on your original drive then drag and drop to the new drive's window. You can also do the drag and drop in one window but for a first timer it is easier to follow with two windows open.
I have a network storage drive in my basement. All of our computers copy to it automatically. Like Sparky says, that's not a real backup. It should be somewhere else. Malware could wipe me out since its connected all the time. If I had a fire, I could certainly lose my backup.
That said, I've been there, done that. I had a bad fire many years ago. I lost pretty much everything. Surprisingly, I recovered all of my files off the hard drive from my melted and fire hosed PC. It was a whopping 40 meg hard drive, haha. Even a fire safe is not the best place to store your backup. My safe left me with readable documents and spendable cash but they were certainly damaged.