If you are not using StoryBoard, you can use the following code:
AppDelegate.swift
import UIKit
@UIApplicationMain
class AppDelegate: UIResponder, UIApplicationDelegate {
    var window: UIWindow?
    var userInputViewContrller: UserInputViewController = UserInputViewController()
    var navigationViewController: UINavigationController = UINavigationController()
    func application(application: UIApplication, didFinishLaunchingWithOptions launchOptions: [NSObject: AnyObject]?) -> Bool {
        self.window = UIWindow.init(frame: UIScreen.mainScreen().bounds)
        self.window?.backgroundColor = UIColor.whiteColor()
        self.navigationViewController = UINavigationController.init(rootViewController: userInputViewContrller)
        self.window?.rootViewController = self.navigationViewController
        self.window?.makeKeyAndVisible()
        return true
    }
Now you have set the rootViewController for window as your naviagationViewController which is initialised with variable for the page "userInputViewContrller"
import UIKit
class UserInputViewController: UIViewController {
    override func viewWillAppear(animated: Bool) {
        let viewFrame = CGRect(x: 1, y: 30, width: 373, height: 635)
        let view: UIView = UIView(frame: viewFrame)
        self.view.addSubview(view)
        let clickMeButton:UIButton = UIButton()
        let nextButtonFrame = CGRect(x: 200, y: 275, width: 150, height: 30)
        nextButton = UIButton(frame: nextButtonFrame)
        clickMeButton.setTitle("Click here", forState: UIControlState.Normal)
        clickMeButton.addTarget(self, action: "clickMeTapped:", forControlEvents: UIControlEvents.TouchUpInside)
        view.addSubview(clickMeButton)
    }
    func clickMeTapped(sender: UIButton){
        let itemViewController = ItemViewController()
        self.navigationController?.pushViewController(itemViewController, animated: true)
    }
}
On click of "Click here" button in UserInputViewController you will be navigated to the next screen itemViewController.
import UIKit
class ItemViewController: UIViewController {
    override func viewWillAppear(animated: Bool) {
        //View
        let viewFrame = CGRect(x: 1, y: 30, width: 373, height: 635)
        let view: UIView = UIView(frame: viewFrame)
        self.view.addSubview(view)
        //Header Label
        let headerLabelFrame = CGRect(x: 25, y: 50, width: 325, height: 30)
        var headerLabel:UILabel = UILabel()
        headerLabel = UILabel(frame: headerLabelFrame)
        headerLabel.text = "Hello I'm in itemViewVireControllr"
        view.addSubview(headerLabel)
  }
}