Q:

How to install SQL Server Express? 

While installing Visual Studio 2010, I saw an option to install SQL Express.  I checked that option assuming it would install SQL Server Express as well, but apparently it didn't.  When I type ssms.exe in Run, it says it cannot find it.  Also, I do not see SQL Server Management Studio under Programs--> Microsoft SQL Server 2008.  All I see is:
Import and Export Data (64 bit)
SQL Server Configuration Manager
SQL Server Error and Usage Reporting
SQL Server Installation Center (64 bit)

When I click on SQL Server Installation Center (64 bit), it asks me to Browse for SQL Server 2008 Installation Media, but I am not sure where it is located at.  

A:

I'm pretty sure SQL Express doesn't include SSMS out of the box. 
You can download Microsoft® SQL Server® 2008 Management Studio Express from Microsoft. 
The error you're reporting does make it seem like it's not fully installed.   You can get an installable stand-alone copy of MSSQL Express 2008 R2 from MS as well, which you could possibly use to repair or reinstall it.