OK, if you have declared your connection string as a string you would access like this:
Dim connectionString As String()
connectionString = 'your connection string'
Dim conn As SqlConnection = New SqlConnection(connectionString)
If you have entered your connection string into the code then you don't need to use the configuration manager as the connection isn't located in the app.config file.
If you have added the connection string to th app.config file you will have a section that look like this:
<?xml version='1.0' encoding='utf-8'?>
<configuration>
<connectionStrings>
<clear ></clear>
<add name="Name"
providerName="System.Data.ProviderName"
connectionString="Valid Connection String;" ></add>
</connectionStrings>
</configuration>
Now you can use the configuration manager to locate the element with the name 'Name' (for example).
If you are having trouble with the idea of app.config files and the storing of connection strings I would suggest typing '.net app confg connection string' into google and reading the MSDN articles that come up.
Hope that helps,