Visual Studio 2005 has no "out of the box" support for SQL Server 2008.  Microsoft has made available an update in the form of a CTP that allow VS 2005 to connect to a SQL Server 2008 CTP5 server.

This CTP resolves a problem that when you try to open a database connection to SQL Server 2008 by using Visual Studio 2005 design tools, you may receive the following error message:
“This server version is not supported. Only servers up to Microsoft SQL Server 2005 are supported.”
This CTP addresses this issue, and enables the following Visual Studio functionality for SQL Server 2008 CTP5 :
 
   Server Explorer successfully connects to SQL Server 2008, and database objects such as stored procedures and table data can be viewed and edited. Note that table schemas still cannot be viewed or edited in this release.
    SQL CLR projects that target SQL Server 2008 CTP5 can be created and deployed to the server.
    T-SQL and SQL CLR debugging are now enabled for SQL Server 2008 CTP5.
    Data binding features in Client and Web Projects are enabled.
 
This CTP does not support the following features for SQL Server 2008 Nov CTP:
 
    Creating and editing table schemas in Table Designer or Database Diagrams. The table designer feature in SQL Server Management Studio 2008 can be used to edit table schemas in SQL Server 2008 CTP5. 

Please download Microsoft Visual Studio 2005 Service Pack 1 Update for Microsoft SQL Server 2008 Support

http://www.microsoft.com/en-us/download/details.aspx?id=15680

 after installing SQL Server Express:

1. install SQL Server Management Studio Express

2. create your database in SSMS Express, give it a logical name (e.g. MyAppDatabase)

3. connect to it using its logical database name (given when you create it on the server) - and don't mess around with physical database files and user instances. In that case, your connection string would be something like:

   Data Source=.\\SQLEXPRESS;Database=MyAppDatabase;Integrated Security=True
   

   and everything else is exactly the same as before..