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
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,