I've followed the "Discovering SQL: A hands on guide for Beginners" instructions and installed SQL Server 2008 Express. However, when following Appendix A, I'm unable to connect to the SQLEXPRESS database. I receive an error stating server was not found.

Obviously I've missed a key instruction.

After creating your database click on your database and look at the properties box on the bottom right of your IDE. In the Connection String row you would have the connection string to your database. Use that connection string in your code to connect to your database.
For more information in connection string go to http://www.connectionstrings.com/.