From SQL Server Management Studio, you cannot connect to a SQL Server Embedded Edition instance by just providing the server name. You need to put the following in the server name input:

\\.\pipe\MSSQL$MICROSOFT##SSEE\sql\query

The files for an embedded edition instance should be at:
C:\WINDOWS\SYSMSI\SSEE\MSSQL.2005\MSSQL\

I have seen multiple people baffled by this question. Hence, I thought I would put up a post about it.