Dafür gibt es die Webclient-Klasse.
Code:
Imports System.Net
Imports System.IO
Private Sub Irgendwas
Dim Client as New Webclient()
Client.Headers.Add("user-agent", "Mozilla/4.0; Windows NT 6.1")
Dim txt As Stream = Client.OpenRead("http://example.org/testfile.txt")
Dim sr As New StreamReader(txt)
...
'Dein weiterer Code hier