You can’t. Instead you should create a WCF service one server that Silverlight can talk to.
Tutorial that does that: http://silverlight.net/learn/tutorials/sqldatagrid.aspx
Your Silverlight app has two projects. One Aspx project for server side, one silverlight on client side.
Your database resides on server side.
You can access it from server side aspx project.
Client side doesn’t know about database.
You can use WCF for connection.
Direct connection is not possible to the database.