Like you said,
1) mount it
2) transfer files
( 3) umount it )
If it's connected, Fedora ought to pick it up at reboot, at least if it's formatted. If not, you need to format it (create partitions if needed). If it's your secondary harddisk, it's device file should be /dev/sdb, and the partitions respectively /dev/sdb1, sdb2, ... if there are more than one partition on the disk.
To mount it manually (in this example, the first partition on the disk; make sure /media/sdb1 directory is created before this):
mount -t fstype /dev/sdb1 /media/sdb1
fstype is the filesystem type the partition has (vfat for FAT filesystem, ntfs for NTFS; note that you probably need to use fuse or something to be able to read-write to ntfs). In some cases the "-t fstype" can be omitted, as that means the fstype is determined automatically, if possible.
But like I said, if you connect the drive and boot your machine after that, Fedora should pick it up automatically and it should show up in your file manager - which is Nautilus, if I'm right.
EDIT: if you need to deal with partitioning/formatting the disk, install and use GParted. It's graphical, easy-to-use program - just remember that the disk you're dealing with must not be mounted when you start working on it.