It is quite difficult and confusing process to install a standalone SQL Server Management Studio 2008.
After you download the setup file, you will see, that it is a 170mb installation package and when you run the installation you will be provided with a full SQL Server Express Intaller.
So how to go on:
-> SQLServer Installation Center
-> Select: New SQL Server stand-alone installation or add features to an existing installation
-> Setup Support Rules - OK
!!! Add features to an existing instanace of SQL Server 2008 - this would be WRONG choice !!!
-> Select: Perfom a new installation of SQL Server 2008
-> Select in the Shared Features: Management Tools - Basic
So even if you have already SQL Server Express intalled you can not add the Management Studio to the features. You have to pretend that you are installing a new copy of SQL Server!
Topic is covered on this blog