下記のコードにて実装可能

Dim mailMessage As New System.Net.Mail.MailMessage("from@gmail.com", "to@gmail.com", "Subject", "Body")

Dim attachment As New System.Net.Mail.Attachment("C:\Temp\これ添付してみる.txt")

mailMessage.Attachments.Add(attachment)

Dim smtpClient As New System.Net.Mail.SmtpClient("smtp.gmail.com")

smtpClient.Credentials = New System.Net.NetworkCredential("xxx@gmail.com", "password")

smtpClient.EnableSsl = True

smtpClient.Port = 587

smtpClient.Send(mailMessage)

添付ファイルを処理する場合は、下記の２行が必要になります。 

Dim attachment As New System.Net.Mail.Attachment("C:\Temp\これ添付してみる.txt")

mailMessage.Attachments.Add(attachment)