The OP is not alone in his puzzlement about the "missing" management client!!! ;-)
The answers by DOK
and CD Jorgensen
found here were -collectively- among the most helpful I found while searching the web on this particular issue! At the risk of being redundant, I'm adding this answer with the goal of being more explicit and of safeguarding the key screenshots from Andrea Montanari's article referenced in DOK's answer.
Two things to know:
Not all installation packages for SQL Server 2008 Express Edition include the Management Studio.
You either need to ...
a)
... download the Install package for SQL Server 2008 Express with Tools (named something like SQLEXPRWT_cpu_language.exe: note the WT
, short for With Tools) or an installer for an Edition of SQL Server other than Express.
or
b)
...download the Installer specific to Microsoft SQL Management Studio Express (same link as provided by CD Jorgensen). This installer only contains the Management Studio; it has none of the SQL Server per se.
[if you go with an a)
install package]
The Management Studio (formerly Enterprise Manager) client remains a stand-alone, independent, component. However its installation is now triggered from a selection made as part of the "Install or Modify SQL Server" track.
It is not found in a separate "Install clients and Tools" menu item from the topmost dialog of the installer (as was the case with SQL 2005 and previous versions).
One should stress that it is stand-alone and the client can indeed be installed on hosts where the SQL Server [engine] is not, and will not be, installed at all. However the initial steps in the Installation Wizard give a strong impression that we will effectively install or re-install SQL Server. It is only on a subsequent step labelled Feature Selection
that we have the ability to select Management Tools
under Shared Features
. On that same Feature Selection dialog we have the option of including or excluding, as desired, the installation of the SQL Server Engine and other Server supporting modules.
These are the two key dialogs of the wizard with regards to this issue:
The first one really appears to put you on track to install or mess with the SQL Server itself, the other dialog finally provides the opportunity of opting for the Client Tools (which include, mainly, the Management Studio). This same dialog also allows checking or un-checking the selection to install the Server per se.

Credits and more info:
The screenshots were taken from Andrea Montanari's article on the Insulin Power web site. This article referenced in DOK's answer provides a step-by-step description of the installation based on the "With Tools" installer.
As said in the introduction, I learned much from CD Jorgensen and DOK's answers; I'm merely making a few things more explicit, here, and correcting a few omissions (e.g. there are some installers which carry both the Server and the client, and it is not necessary to install the server).