Open a file that is located on another computer

As Abdul already stated if you have the correct credentials it's quite easy. Another requirement would be to be on the LAN or have a VPN tunnel to said system it's also possible you there is a remote connection server running on your server and a remote desktop client on your local machine.

I'll go with the simplest solution though that relies on the process accessing the file running with administrative privelidges: You can use this to access the files on the server.

Dim fileName as String
'On every server there are administrative shares for all drives
fileName = @"\\ServerName\c$\temp\file.txt"
Dim fs as new FileStream(fileName)
Dim sr as new StreamReader(fs)
Dim line as String
Do
    line = sr.ReadLine()
    Console.WriteLine(Line)
Loop Until line Is Nothing

If there are drives D,E and F then these would be accessible by shares d$, e$ and f$. The alternative is to have somebody (server administrator for instance) set up a share that lets you access the files you need.

Hope that helps you!

Cheers,