After many hours of sifting through MSDN help, I finally stumbled across the solution:

' Declare an instance of the web service
Dim oWebSrvc As New n_intranet.Data()
' Tell it to use a different URL
oWebSrvc.Url = "http://www.newserver.com/newwebsrvice.asmx"

Why is it that something so simple can take days to figure out?