OdbcConnectionStringBuilder を使っている以外は特別なところはありません。
OdbcConnection の使い方と、接続のサンプルです
Imports System.Data.Odbc

Module Module1

	Sub Main()

		' 新しい OdbcConnectionStringBuilder オブジェクトを作成
		Dim builder As New OdbcConnectionStringBuilder()

		' ドライバ文字列をセット ( 波型括弧{} は必要ありません ) 
		builder.Driver = "MySQL ODBC 5.1 Driver"

		' 接続用のパラメータを追加
		builder.Add("SERVER", "localhost")
		builder.Add("DATABASE", "lightbox")
		builder.Add("UID", "root")
		builder.Add("PWD", "password")

		' 内容を確認

		' 新しい OdbcConnection オブジェクトを作成
		Dim myCon As New OdbcConnection()

		' 接続文字列を設定
		myCon.ConnectionString = builder.ConnectionString

		' 接続を開く
		Catch ex As OdbcException
			' Console.WriteLine( ex.Message )
			Call ErrorAction( ex )
			Exit Sub
		End Try

		' 接続を閉じる

		' OdbcConnection オブジェクトに使用されているすべてのリソースを解放

		' 処理終了

		' 一時停止
		Console.Write("Enterキーを押して下さい : ")

	End Sub

	' ******************************************************
	' エラー処理
	' ******************************************************
	Sub ErrorAction( ex As OdbcException )

		Dim CrLf As String = ControlChars.CrLf
		Dim errorMessages As String = ""
		Dim i As Integer

		For i = 0 To ex.Errors.Count - 1
			errorMessages &= _
				"Index #" & i.ToString() & CrLf _
				& "Message: " & ex.Errors(i).Message & CrLf _
				& "NativeError: " & ex.Errors(i).NativeError.ToString() & CrLf _
				& "Source: " & ex.Errors(i).Source & CrLf _
				& "SQL: " & ex.Errors(i).SQLState & CrLf
		Next i


	End Sub

End Module

パラメータは、Microsoft の標準のものを使用していますが、MySQL が定義したものを利用できます。
        builder.Add("SERVER", "localhost")
        builder.Add("DATABASE", "lightbox")
        builder.Add("USER", "root")
        builder.Add("PASSWORD", "password")
        builder.Add("PORT", "3306")
Parameter Comment
user The user name used to connect to MySQL.
uid Synonymous with user
server The host name of the MySQL server.
database The default database.
option Options that specify how Connector/ODBC should work. See below.
port The TCP/IP port to use if server is not localhost.
initstmt Initial statement. A statement to execute when connecting to MySQL. In version 3.51 the parameter is called stmt. Note, the driver supports the initial statement being executed only at the time of the initial connection.
password The password for the user account on server.
pwd Synonymous with password
socket The Unix socket file or Windows named pipe to connect to if server is localhost.
sslca The path to a file with a list of trust SSL CAs. Added in 3.51.16.
sslcapath The path to a directory that contains trusted SSL CA certificates in PEM format. Added in 3.51.16.
sslcert The name of the SSL certificate file to use for establishing a secure connection. Added in 3.51.16.
sslcipher A list of permissible ciphers to use for SSL encryption. The cipher list has the same format as the openssl ciphers command Added in 3.51.16.
sslkey The name of the SSL key file to use for establishing a secure connection. Added in 3.51.16.
charset キャラクタセット設定
sslverify If set to 1, the SSL certificate will be verified when used with the MySQL connection. If not set, then the default behavior is to ignore SSL certificate verification.
readtimeout The timeout in seconds for attempts to read from the server
writetimeout The timeout in seconds for attempts to write to the server
interactive Enables the CLIENT_INTERACTIVE connection option of mysql_real_connect.

VB.net 2008 : System.Data.Odbc 更新処理( MySQL 5.1 )