How to connect my sql database to query when published my asp.net website

You can publish the local mdf file to your target server . The connection string/settings should be changed accordingly. Refer the following on how to do it.

http://www.asp.net/web-forms/tutorials/deployment/deploying-web-site-projects/deploying-a-database-cs[^]

Try and revert if stuck somewhere.
Hope this helps

You can install the "Connector/Net 1.0 (.NET)" from the mysql website:

http://www.mysql.com/downloads/connector/net/

and transfer the MySql.Data.dll, MySql.Data.Entity.dll, and MySql.Web.dll to the bin folder of your project.

Here is the new code that you can use to connect and finaly display your database online.
This works on godaddy:
using System;
using System.Collections.Generic;
using System.Linq;
using System.Web;
using System.Web.UI;
using System.Web.UI.WebControls;

//Include namespaces for the MySql .Net Connector
using MySql.Data.MySqlClient;
using System.Data;
using System.Data.SqlClient;


namespace WebApplication1
{
public partial class _Default : System.Web.UI.Page
{
protected void Page_Load(object sender, EventArgs e)
{
string connectionString =
"Server=####.db.####.####.com; " +
"Port=####; Database=####; Uid=####; Pwd=####;";

//Create a connection object
MySqlConnection mySqlConnection = new MySqlConnection(connectionString);

//Create a connection command
MySqlCommand mySqlCommand = new MySqlCommand("SELECT * FROM mytable", mySqlConnection);

//check the connection state and open it accordingly.
if (mySqlConnection.State == ConnectionState.Closed)
mySqlConnection.Open();

//MySql datareader object to read the stream of rows from SQL Server Database
MySqlDataReader myDataReader = mySqlCommand.ExecuteReader();

//Pass the Sql DataReader object to the DataSource property
//of DataList control to render the list of items.
myDataGrid.DataSource = myDataReader;
myDataGrid.DataBind();

// close the Sql DataReader object
myDataReader.Close();

// check the connection state and close it accordingly.
if (mySqlConnection.State == ConnectionState.Open)
mySqlConnection.Close();

}

}
}