You shouldn't be doing backups by dealing with the raw MySQL files. It's trivially easy to end up with a corrupted database that way. Consider what happens when you start copying the files to your backup medium - the copy will take a non-zero amount of time, during which the database could potentially write new data in various places, including the parts you've already copied. Now you're copying a modified file, a mix of old data and new data. This modified copy is almost guaranteed to be corrupted.
You should be using mysqldump or mysqlhotcopy instead, which guarantee a consistent backup.
However, on the chance that your database is relatively quiet and you managed to get a good clean backup copy, the files you need to restore depend on the type of tables you're restoring. InnoDB stores all of its data in the ib*
files, regardless of database/table name. MyISAM uses files in directories named according to the database/table names.
After copying the backup copies into the correct locations, you'll have to restart MySQL, as it will still be accessing the original copies of the files.