Ok, I finally figured it out. There is a property called Request.Files, It holds all of the data on the files that are being uploaded to that page. You can then loop through it and save the files to the web server. Code for anyone interested:
Partial Class _Default
Inherits System.Web.UI.Page
Protected Sub Page\_Load(ByVal sender As Object, ByVal e As System.EventArgs) Handles Me.Load
If Me.Request.Files.Count <> 0 then
Dim I As Integer
For I = 0 To Me.Request.Files.Count - 1
Me.Request.Files.Item(I).SaveAs("C:\\some\\path\\Uploads\\" & Me.Request.Files.Item(I).FileName)
Next
End If
End Sub
End Class
I'm not sure that's the best way to go about it, but it works! I think I may write up an article about this as I couldn't find this information easily ANYWHERE.