El siguiente ejemplo utiliza ASP.NET (VB o C#) para conectarse a Mysql

Archivo: web.config valido para Visual Basic o C#.

<?xml version="1.0" encoding="utf-8"?>
<configuration>
  <system.web>
    <compilation strict="false" explicit="true" targetFramework="4.6.1"/>
    <httpRuntime targetFramework="4.6.1"/>
    <customErrors mode="Off"/>
  </system.web>
     <connectionStrings>
        <add name="micadenamysql" connectionString="Server=localhost;Port=3306;Database=midomin_mibase;Uid=midomin_admin;Pwd=123456" providerName="MySql.Data.MySqlClient"></add>
    </connectionStrings>
</configuration>

Archivo: WebForm1.aspx si utiliza Visual Basic

Imports MySql.Data.MySqlClient
Public Class WebForm1
    Inherits System.Web.UI.Page
    Protected Sub Button1_Click(ByVal sender As Object, ByVal e As EventArgs) Handles Button1.Click
        Dim connection As MySqlConnection
        connection = New MySqlConnection
        'se apunta a la cadena de conexion guardada en el archivo Web.config
        connection.ConnectionString = System.Configuration.ConfigurationManager.ConnectionStrings("micadenamysql").ConnectionString
        Try
            connection.Open()
            Label1.Text = "Conectado a mysql"
            Try
                Dim ComandoSQL As New MySqlCommand("Select * From personas", connection)
                Dim ds As New DataSet
                Dim da As New MySqlDataAdapter(ComandoSQL)
                da.Fill(ds)
                GridView1.DataSource = ds.Tables(0)
                GridView1.DataBind()
                Label1.Text = "Informacion cargada"
            Catch
                Label1.Text = "Conectado a mysql, pero: error en consulta"
            End Try
        Catch ex As Exception
            Label1.Text = "Error " & ex.Message
        End Try
    End Sub
End Class

Archivo: WebForm1.aspx si utiliza C# (C Sharp)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Web;
using System.Web.UI;
using System.Web.UI.WebControls;
using MySql.Data.MySqlClient;
using System.Data;

namespace miproyecto
{
    public partial class WebForm1 : System.Web.UI.Page
    {
        protected void Button1_Click1(object sender, EventArgs e)
        {
            MySqlConnection connection = default(MySqlConnection);
            connection = new MySqlConnection();
            //se apunta a la cadena de conexion guardada en el archivo Web.config
            connection.ConnectionString = System.Configuration.ConfigurationManager.ConnectionStrings["micadenamysql"].ConnectionString;
            try
            {
                connection.Open();
                Label1.Text = "Conectado a mysql";
                try
                {
                    MySqlCommand ComandoSQL = new MySqlCommand("Select * From personas", connection);
                    DataSet ds = new DataSet();
                    MySqlDataAdapter da = new MySqlDataAdapter(ComandoSQL);
                    da.Fill(ds);
                    GridView1.DataSource = ds.Tables[0];
                    GridView1.DataBind();
                    Label1.Text = "Informacion cargada";
                }
                catch
                {
                    Label1.Text = "Conectado a mysql, pero: error en consulta";
                }
            }
            catch (Exception ex)
            {
                Label1.Text = "Error " + ex.Message;
            }

        }
    }
}