mgb
Unpack the file with the tar command
man tar
for specifics
databases are usually in
/var/lib/mysql/...
They should be in a dump file in
/home/e-smith/db
or is it
/home/e-smith/db/mysql
if the correct pre backup event was run on the server you were backing up.
Did you run the pre restore event on the new server, you need to do this to delete old copies of previous database dumps.
PS
If you can backup only user passwords and email user - Example
You cannot easily backup just that data, it is scattered throughout many files on the server & all of those have to be restored as an intact set as they cross correlate to each other with system IDs etc.
That's why you should (MUST) follow the standard backup & restore procedures & file inclusions as outlined in the Backup server config Howto
http://wiki.contribs.org/Backup_server_config#Standard_backup_.26_restore_inclusionsand this here
http://wiki.contribs.org/Backup_server_config#Manually_transferring_configuration_informationis the correct procedure to use to do a full backup & restore manually.
Deviation from these (as you are doing) will cause loss of data & loss of data entries & loss of mysql databases & tables & other information, users, ibays etc.
You have been WARNED.