Обычная строка будет скопирована через
UIPasteboard *pasteboard = [UIPasteboard generalPasteboard];
pasteboard.string = @"my test string";
URL через, например,
UIPasteboard *pasteboard = [UIPasteboard generalPasteboard];
pasteboard.URL = [NSURL URLWithString:@"/3387703/iphone-skopirovat-chto-nibud-v-bufer-obmena-s-pomoschy-koda"];