The sample in the document doesn't show you how to directly access a property you know the name of.
Given the following <appSettings> snippet in your web.config:
<!-- put this right after </configSections> -->
<appSettings>
<add key="AdminEmail" value="admin@example.com"/>
</appSettings>
<!-- this should be just before <connectionStrings> -->
Then you can access it like this:
C#:
string AdminEmail = ConfigurationManager.AppSettings["AdminEmail"];
VB.NET:
Dim AdminEmail As String = ConfigurationManager.AppSettings("AdminEmail")