You can start a process to add the network drive. Then you can check to see when and how p finishes.
Dim p As Process
p = System.Diagnostics.Process.Start("net.exe", "use r: \\reo\c-drive")
Here is one way to check the availability of a drive letter:
If System.IO.Directory.Exists("c:\") Then ...
You can also use Windows API calls, which are messier to write but don't require a separate process.
It's usually not necessary to map a network drive, however, because you can generally use the network path instead of the mapped drive letter.