I assume you installed Fedora using the defaults which means the disks are formatted with a LVM partition. You can verify by via the GUI LVM manager or by examining the output of the console command fdisk command:
fdisk -l (That is a small L and you must be root)
If you are using LVM then it is a little more complicated to mount the old drive then a regular partition as suggested in the previous post. As indicated in the link you will need to change the volume group name before it can be mounted on your new computer.
http://fedoraproject.org/wiki/JohnBabich/Mount_LVM