What is a built in database? What should I do to get a copy of my MS SQL database in the solution explorer window in Visual Studio 2008 so that when I copy the solution folder the database files will be copied with it?
A built-in database is something along the lines of SQLite, or the deprecated MS Access Jet engine; a system that allows access to a database structure without relying on an external program.
That answers your "what is" question. The rest depends on what you're doing, which is confusing.
I think the built in database for VS uses Sql Server Express Edition.
The simple answer would be to Click on Project/Add New Item choose Data and then select the type you want. LINQ to SQL will probably be the simplest to start with.
For ADO.Net select "Dataset". Then from the Server Explorer you may add a connection to you data. From that point you just drag and drop.
Install SQL Server Express from http://www.microsoft.com/express/.
Besides the already mentioned SQL Express, you can also use SQL Server Compact Edition.
From the MS SQL Server site "SQL Server Compact 3.5 is a free, easy-to-use embedded database engine that lets developers build robust Windows Desktop and mobile applications that run on all Windows platforms including Windows XP, Vista, Pocket PC, and Smartphone."
There is aslo a comparsion document between the Compact and Express editions on the SQL Server site.