It's just a UIViewController presented modally with the popup's view controller modalPresentationStyle
set to UIModalPresentationFormSheet
.
MyPopupViewController *popup = ...
popup.modalPresentationStyle = UIModalPresentationFormSheet;
[self presentModalViewController:popup animated:YES];
From the docs regarding UIModalPresentationFormSheet
presentation style...
The width and height of the presented view are smaller than those of
the screen and the view is centered on the screen. If the device is in
a landscape orientation and the keyboard is visible, the position of
the view is adjusted upward so that the view remains visible. All
uncovered areas are dimmed to prevent the user from interacting with
them.
You'll need to detect touches on the darkened area to allow the form to be dismissed that way. This answer has some details on implemented that.