Or alternatively if you have access to the administrative share:
My.Computer.FileSystem.CopyFile("C:\File.txt", "\\computerName\C$\File.txt")
(System.IO.File.Copy works similarly but does not use the Shell32 UI to show progress as the above method does.)
This will copy local C:\File.txt to remote C:\File.txt.
Or use System.DirectoryServices to quickly create a share, or use WMI to do the same. But if you can create a share on the remote computer, you should already have access to the administrative share unless disabled or restricted via group policy.