SQL Server Express 2012

If you have not installed it previously install SQL SERVER EXPRESS 2012 with the Management Studio. Make sure you select either SQLEXPRWT_x64_ENU.exe if you have a 64 bit version of Windows or SQLMEXPRWT_x86_ENU.exe, if you have a 32 bit version of Windows.
To check which version of Windows you have goto Computer in the windows explorer and right click, and select properties
If you have already installed SQL Server Express 2012 without the management studio then install the Management Studio using either SQLManagementStudio_x64_ENU.exe if you have a 64 bit version of Windows or SQLManagementStudio_x86_ENU.exe, if you have a 32 bit version of Windows.
If you already have a previsous version of SQL EXPRESS installed you can opt to upgrade that to SQL EXPRESS 2012, in which case you can use the default name of for the server of SQLEXPRESS. This might be the best option as Visual Studio assumes that to be the server name.
If you have no previous version, or if you wish to retain the previous version, select New Instance (or for installing the Management studio on top of SQL EXPRESS). If you have a previous version call this version SQLEXPRESS2012. After the installation you will need to change the Tools, Options, Database Connections settings to SQLEXPRESS2012 as shown below.