NSFileManager and NSWorkspace both have methods to move, copy, and delete files. Usually you’d use NSFileManager since its easier to work with:
if ( [[NSFileManager defaultManager] isReadableFileAtPath:source] )
[[NSFileManager defaultManager] copyItemAtURL:source toURL:destination error:nil];
However, NSWorkspace can easily move files to the Trash, which NSFileManager can’t do.
[[NSWorkspace sharedWorkspace] performFileOperation:NSWorkspaceRecycleOperation source:foldername destination:@"" files:filenamesArray tag:&tag];
Check the documentation for a more complete description of the two classes. (NSFileManager, NSWorkspace)