You can not use any ADO.NET classes (infact they are not included in sl) inside silverlight (sl), because the silverlight is in user's browser, and your ADO.NET can be in your server...
silverlight application is a Rich Intenet Application (RIA), means it has rich set of user interaction tools inside the browser, whatever happens can only happen in browser... or it call make call to services i.e. ASP.NET webservice, WCF services, RIA services.. etc...
its a good place to learn silverlight/wpf...
go through it. :)
http://www.wpftutorial.net/[
^].
if satisfied mark as answer.. for more clarifications comment below :)