The way it is done is to populate second dropdown in SelectedIndexChanged event of the first dropdown
Example:  
Protected Sub ddlCountry_SelectedIndexChanged(ByVal sender As Object, ByVal e As EventArgs)
    Dim CountryID As Integer = Convert.ToInt32(ddlCountry.SelectedValue.ToString())
    FillStates(CountryID)
End Sub
Private Sub FillStates(ByVal countryID As Integer)
  Dim strConn As String = ConfigurationManager.ConnectionStrings("DatabaseConnectionString").ConnectionString
  Dim con As New SqlConnection(strConn)
  Dim cmd As New SqlCommand()
  cmd.Connection = con
  cmd.CommandType = CommandType.Text
  cmd.CommandText = "Select StateID, State from State where CountryID =@CountryID"
  cmd.Parameters.AddWithValue("@CountryID", countryID)
  Dim objDs As New DataSet()
  Dim dAdapter As New SqlDataAdapter()
  dAdapter.SelectCommand = cmd
  con.Open()
  dAdapter.Fill(objDs)
  con.Close()
  If objDs.Tables(0).Rows.Count > 0 Then
    ddlState.DataSource = objDs.Tables(0)
    ddlState.DataTextField = "State"
    ddlState.DataValueField = "StateID"
    ddlState.DataBind()
    ddlState.Items.Insert(0, "--Select--")
  Else
    lblMsg.Text = "No states found"
  End If
 End Sub
With html source as so:
   <asp:DropDownList ID="ddlState" runat="server" AutoPostBack="True">
  </asp:DropDownList>
  <asp:DropDownList ID="ddlCountry" runat="server" 
  AutoPostBack="True" OnSelectedIndexChanged="ddlCountry_SelectedIndexChanged">
 </asp:DropDownList>