SQL Server Express Setup
Open SQL Server Configuration Manager (Start > Programs > Microsoft SQL Server 2012 > Configuration Tools). Look at the SQL Server Services node; you should see something like this:


  


If that right pane is empty, or if you can't find Configuration Manager installed at all, then you don't have SQL Server installed. Go download the latest version (SQL Server 2014) from here:

http://www.microsoft.com/en-us/download/details.aspx?id=42299

You want ExpressAndTools 64BIT\SQLEXPRWT_x64_ENU.exe, unless you're on a 32-bit system for some reason, then you want ExpressAndTools 32BIT\SQLEXPRWT_x86_ENU.exe.

Download that, and try the setup again. You may not be able to name this instance SQLEXPRESS; that's okay, some people have many instances installed and they can't all have the same name.