Newbie having a couple hiccups

Right now it does not appear to be mounted anywhere.

And I would guess we are talking about this device?

Again its not currently mounted to anything.

But the normal default would probably be /run/media/$USER/$PART-LABEL

Once it is mounted (such as by clicking it in your file manager) it will appear at its mountpoint, likely the one above.

If you want it to be automatically mounted all the time I would suggest adding it to /etc/fstab or using systemd to do it for you.

The archwiki fstab page will have most all information needed for that:

https://wiki.archlinux.org/title/Fstab

For systemd mounts there is a guide here on the forum: