I'm doing an app and I was wondering how can you show a view like this:

That would be called a sheet. This guide should walk you through how to do them.
You basically make a NSWindow that you would like to use as a sheet, then, when you want to show it, call:
[NSApp beginSheet: myCustomSheet modalForWindow: window modalDelegate: self didEndSelector: @selector(didEndSheet:returnCode:contextInfo:) contextInfo: nil];`
myCustomSheet is obviously your sheet and window is the window you want it to appear in. Set self as the delegate and implement didEndSheet:returnCode:contextInfo::
- (void)didEndSheet:(NSWindow *)sheet returnCode:(NSInteger)returnCode contextInfo:(void *)contextInfo
{
[sheet orderOut:self];
}
Hook up a "close" button on your sheet to an IBAction that closes the sheet.
- (IBAction)closeMyCustomSheet: (id)sender
{
[NSApp endSheet:myCustomSheet];
}
These sheets don't even need to be folded! XD