Basically, it's just a case of calling File.Move: File.Move Method (String, String) (System.IO)
] and providing the source and destination paths.
The problems occur if the remote machine requires a login, in which case the simplest solution is to create a "virtual disk" on your PC which is connected to the folder on the remote PC (I do this to my NAS to make everything simpler, and connect "drive letters" to a number of different folders for various purposes). You can do this in Windows Explorer, via the "Map network drive" option of the network context menu.
If you don't, then you probably need to use impersonation:
WindowsIdentity wid = new WindowsIdentity(username, password);
WindowsImpersonationContext context = wid.Impersonate();