Open AppStore through button

Here. But I highly suggest you learn the basics of Swift!

UIApplication.sharedApplication().openURL(NSURL(string: "itms://itunes.apple.com/de/app/x-gift/id839686104?mt=8&uo=4")!)

If you wanna open the AppStore in Swift 5:

if let url = URL(string: "itms-apps://itunes.apple.com/app/id1629135515") {
    UIApplication.shared.open(url)
}

I use this combination, its better for rate/shopping.

(partially from here)

    @IBAction func rateMe(sender: AnyObject) {
    if #available(iOS 8.0, *) {
        openStoreProductWithiTunesItemIdentifier("107698237252");
    } else {
        var url  = NSURL(string: "itms://itunes.apple.com/us/app/xxxxxxxxxxx/id107698237252?ls=1&mt=8")
        if UIApplication.sharedApplication().canOpenURL(url!) == true  {
            UIApplication.sharedApplication().openURL(url!)
        }

    }
}
func openStoreProductWithiTunesItemIdentifier(identifier: String) {
    let storeViewController = SKStoreProductViewController()
    storeViewController.delegate = self

    let parameters = [ SKStoreProductParameterITunesItemIdentifier : identifier]
    storeViewController.loadProductWithParameters(parameters) { [weak self] (loaded, error) -> Void in
        if loaded {
            // Parent class of self is UIViewContorller
            self?.presentViewController(storeViewController, animated: true, completion: nil)
        }
    }
}
func productViewControllerDidFinish(viewController: SKStoreProductViewController) {
    viewController.dismissViewControllerAnimated(true, completion: nil)
}

don't forget to import and delegate:

import StoreKit

class RateMeViewController: UIViewController, SKStoreProductViewControllerDelegate {

Swift 3 Syntax and improved with an 'if let'

if let url = URL(string: "itms-apps://itunes.apple.com/app/id1024941703"),
UIApplication.shared.canOpenURL(url){
    UIApplication.shared.openURL(url)
}

UPDATE 7/5/17 (Thank you Oscar for pointing this out):

if let url = URL(string: "itms-apps://itunes.apple.com/app/id1024941703"),
    UIApplication.shared.canOpenURL(url)
{
    if #available(iOS 10.0, *) {
        UIApplication.shared.open(url, options: [:], completionHandler: nil)
    } else {
        UIApplication.shared.openURL(url)
    }
}