Hi marutivsn,

First, add connection string in Web.Config file in ASP.Net Web Forms Application.

If you are working with Windows applications, then use App.Config.

For more details on how to add connection string, please refer below articles.

ASP.Net Web Forms: 

Read or Write Connection Strings in Web.Config file using ASP.Net using C# and VB.Net

ASP.Net Windows:

.Net 4.5: Read (Get) Connection String from App.Config file using C# and VB.Net

Connecting Database in Code using VB.Net

You need to make use of SqlConnection and SqlCommand class as they are use for connecting your application to server or database.

'Specifying Sql query
Dim query As String = "<SQL QUERY>"

'Fethced database or server details from Web.Config or App.Config.
Dim constr As String = ConfigurationManager.ConnectionStrings("constr").ConnectionString

'Making connection to the database or server
Using con As SqlConnection = New SqlConnection(constr)

    'For executing Sql query
    Using cmd As SqlCommand = New SqlCommand(query, con)
        'Perform Database Operations here.
    End Using
End Using

For practical example, refer my article 

Bind data to ASP.Net GridView using Stored Procedure