If your new disk doesn't have the same partitions or organization as the old disk, modify the file /new-disk/etc/fstab on the new disk as appropriate.
Make sure that the disk partitions (first column) correspond to the organization you'll have with the new disk, once the old disk has been removed, and that you're only mounting one partition at / as shown in the second column.
For more information on the format of the file /etc/fstab, see the Linux System Administrator's Guide, section 4, under Mounting and unmounting.
For swap partitions, use a line similar to this one:
/dev/hda1 swap swap defaults 0 0