How to transition to a new view controller with code only using Swift

The problem is that your code is creating a blank UIViewController, not a SecondViewController. You need to create an instance of your subclass, not a UIViewController,

func transition(Sender: UIButton!) {   
    let secondViewController:SecondViewController = SecondViewController()

    self.presentViewController(secondViewController, animated: true, completion: nil)

 }

If you've overridden init(nibName nibName: String!,bundle nibBundle: NSBundle!) in your SecondViewController class, then you need to change the code to,

let sec: SecondViewController = SecondViewController(nibName: nil, bundle: nil)