a Where clause in db query datetime = string

Personally, I'd use one of the technologies .Net offers for passing parameters into database queries. Use of parameters ensures that things like date formats and strings are handled correctly; they are also essential for preventing SQL injection attacks when your filter values are captured as text from a user.

Here's an old-school approach, Linq and Entity Framework offer ways to do it that are more OO but can hide what's going on between your app and the database (not always a problem, but it doesn't help when you're trying to learn concepts):

public static void DoStuff()
{
    const string CONNECTION = "write me - the connection string";
    const string SQL = "SELECT * "+
                        " FROM table "+
                        " WHERE date_deliv_required = @DateDelivered";

    var dateDelivered = Convert.ToDateTime("01/08/2008");

    DataTable dt = new DataTable();
    using (var conn = new SqlConnection(CONNECTION))
    {
        using (var cmd = new SqlCommand(SQL, conn))
        {
            conn.Open();
            cmd.Parameters.AddWithValue("@DateDelivered", dateDelivered);
            cmd.CommandType = CommandType.Text;
            using (var ada = new SqlDataAdapter(cmd))
            {
                ada.Fill(dt);
            }
        }
    }

    // Do stuff with the rows in the data table dt...
}