Restoring a backup to an older version of SQL Server
You'd have use the Import/Export wizards in SSMS to migrate everything
There is no "downgrade" possible using backup/restore or detach/attach
You can use the Import/Export wizard to move data between databases.
Right click on the database you want to export, choose "Tasks", then "Export Data". The wizard will guide you through the process.
You're right, though. You won't be able to do a backup/restore moving from SQL Server 2008 R2 to SQL Server 2008 Express.
SQL Server backup doesn't support backward compatibility
Steps to get DB on older versions -
For Schema: right click on your database --> Tasks --> generate scripts -->next-->next--> click on advanced button --> change the option "type Of Data to script" to "schema" -->ok -->next -->next
For Data: right click on your database --> Tasks --> generate scripts -->next-->next--> click on advanced button --> change the option "type Of Data to script" to "data" -->ok -->next -->next