Update 20 may 2009: New easy solution
Set the Connection -> Application Settings property True. This will generate a connection string in your app.config.

Copy this connection string to your web.config and you're all set!
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Old post:
If you want to use your connectionstring from the web.config with Linq to Sql (dbml) you have to add the following partial class to your project:
[code:c#]
namespace Your.Namespace
{
partial class ***yourDataContext
*** {
partial void OnCreated()
{
ConnectionStringSettings s = ConfigurationManager.ConnectionStrings["YourConnectionString"];
if (s != null)
Connection.ConnectionString = s.ConnectionString;
}
}
}
[/code]
Don't forget to change the Your.Namespace, yourDataContext and YourConnectionString to fit your project.
Hope this helps.