Hello Paul, and welcome!
You do not need to format your hard drive to back up your files from it using restic. Doing so would be rather counter-productive 
Jokes aside, I presume you meant the/a hard drive that you intend to use for storing your backups on? In that case, you don’t need to format it in any special way - just have it formatted in the way that is most suitable for the system you are backing up from and the system(s) you might want to restore to - you want them to be able to read the disk when you need to restore from it.
To install restic, you can either use Homebrew or simply download and run the latest pre-compiled restic binary from the restic release page.
Once you have restic installed or downloaded, you need to run it, and this is something you do from the command line. There are primarily two steps - first you create your backup repository (where your backups are stored), and then you start backing up your files to that repository.
Creating your backup repository is described here, and backing up is described here.
To delete old snapshots that you don’t want, you use the forget and prune commands, which is described here.
Regarding which type of repository to chose, and where to put it, I’d say you naturally want it to be placed somewhere else than on the same computer you are backing up. At the very least a separate hard drive, but it’s probably better if you can get your backups stored offsite somewhere, e.g. on Amazon S3 or any of the other cloud backends restic supports.
Restic will soon also support using rclone as backend, which will give you access to all the backends that rclone supports (see list on the previous link) - pretty awesome!
That said, yes, using restic currently involves a bit of using the terminal/command line. But it’s not that bad - restic is super easy to install and after that it’s literally just a couple of commands to have your system backed up - don’t let them scare you off.
As an additional reference, here’s a guide on how to schedule restic on macOS, by @matt: Example: Scheduling regular backups on macOS
Feel free to ask follow-up questions!