How can I clone an SQL Server database on the same server in SQL Server 2008 Express?

1. Install Microsoft SQL Management Studio, which you can download for free from Microsoft's website:

   Version 2008

   Microsoft SQL Management Studio 2008 is part of SQL Server 2008 Express with Advanced Services

   Version 2012

   Click download button and check ENU\x64\SQLManagementStudio_x64_ENU.exe

   Version 2014

   Click download button and check MgmtStudio 64BIT\SQLManagementStudio_x64_ENU.exe

2. Open Microsoft SQL Management Studio.

3. Backup original database to .BAK file (db -> Task -> Backup).
4. Create empty database with new name (clone). Note comments below as this is optional.
5. Click to clone database and open restore dialog (see image)
6. Select Device and add the backup file from step 3.
7. Change destination to test database
8. Change location of database files, it must be different from the original. You can type directly into text box, just add postfix. (NOTE: Order is important. Select checkbox, then change the filenames.)
9. Check WITH REPLACE and WITH KEEP_REPLICATION

Right-click the database to clone, click Tasks, click Copy Database.... Follow the wizard and you're done.

You could try to detach the database, copy the files to new names at a command prompt, then attach both DBs.

In SQL:

USE master;
GO 
EXEC sp_detach_db
    @dbname = N'OriginalDB';
GO

At Command prompt (I've simplified the file paths for the sake of this example):

copy c:\OriginalDB.mdf c:\NewDB.mdf
copy c:\OriginalDB.ldf c:\NewDB.ldf

In SQL again:

USE master;
GO
CREATE DATABASE OriginalDB
    ON (FILENAME = 'C:\OriginalDB.mdf'),
       (FILENAME = 'C:\OriginalDB.ldf')
    FOR ATTACH;
GO
CREATE DATABASE NewDB
    ON (FILENAME = 'C:\NewDB.mdf'),
       (FILENAME = 'C:\NewDB.ldf')
    FOR ATTACH;
GO