I am very intrigued by this new version of SQL Server Express.
It's not clear (to me) what a setup program should do to deploy an application that use a LocalDB.
Is it required to install SQL Server Express on the client PC and then attach the MDF file?
Or it's only required to run the LocalDB.msi
and it works as a standalone file like SQL Server Compact?
You don't need to install SQL Server Express to use LocalDB, as LocalDB is SQL Server Express, just easier to install.
Once LocalDB is installed you can use AttachDbFileName property of the connection string to "open" an MDF file. Keep in mind that the same file can only be opened by a single LocalDB instance (single Windows login) at any given time, so this is not a data-sharing feature.
Update: If your application is using .NET, make sure to install .NET 4.0.2 or newer, as mentioned here. The original .NET 4 doesn't understand LocalDB connection strings, as it shipped long before LocalDB.